For the record, I am no longer working in Chinese universities, and I'm not from the fields of math or CS. A few years ago, I was doing a tenure-track position in a university in one of the top 5 largest Chinese cities. I am merely writing this answer since no one else has come to the fore, but I am hoping that someone who has direct experience of doing a postdoc in China can come here to give more accurate info. All I can do is provide a rough outline and some words of advice.
In recent years, China has been implementing a new system of recruitment roughly known as the "pre-hired/long-term hired" system (预聘/长聘). Note however that depending on the university, you can see other variants of these names such as 准聘, 校聘, or 特聘, all of which have their own specificities. more information on these terms can be found in this Chinese website (use Google Translate, it should give you a good idea).
Basically speaking, "pre-hired" is the Chinese equivalent to being on the tenure-track system, and "long-term hired" means that one becomes officially tenured faculty.
Even though these recruitments are written in English, their main objective is to attract Chinese mainland students who graduated from top universities overseas, since they are likely to be more supportive of local politics and better-integrated into the country's culture. That said, you can apply and you will be certainly considered for a position.
The actual system of recruitment and its details vary somewhat from university to university, but for most universities there are usually two key periods throughout the year when the university is receiving CVs from Chinese and foreign candidates, and conducts interviews to decide who will be hired. Some universities appear to receive CVs all year long.
Each time, there is a limited quota of positions that can be filled. Universities in China are feverishly expanding their campuses into new locations, and are desperate to hire faculty members who can push the university up on the THE rankings or QS World Rankings. Key points are to publish as many papers as possible in SSCI journals, and attract foreign staff from top international institutions.
Regarding rank names, this "pre-hired/long-term hired" system has two variants: for the sake of convenience, let's call them the "old system" and "new system".
I do not recall the exact Chinese names of all the ranks, so I will just write the English ones.
Old system, from low to high rank:
(5) Adjunct Researcher/Post-doc
(4) Assistant Teacher (equivalent to lecturer/instructor in USA, adjunct position)
(3) Lecturer (roughly equivalent to an Assistant Professor in the USA)
(2) Associate Professor
(1) Full Professor
New system, low to high rank:
(5) Vice-Researcher (equivalent to postdoc)
(4) Associate Researcher (roughly equivalent to Lecturer, but usually with better salary, this is a tenure-track position)
(3) Assistant Professor (can be both tenure-track or a fully tenured position)
(2) Associate Professor (can be both tenure-track or a fully tenured position)
(1) Full Professor (can be both tenure-track or a fully tenured position)
In order for you to be accepted into a tenure-track position, you are required to have obtained a PhD from one of the top 200 institutions in the World University Rankings, and must have spent at least 2 years of research experience in a university or research institution. These two years can be spent either as a "Post-Doc", or as a position with a similar title such as "Researcher", "Assistant Researcher", "Lecturer", etc. This requirement is pretty strict, although with the right connections, it may be possible that some exceptions can be made.
What normally happens after you sign the contract as a post-doc or as a tenure-track faculty member, is that you are expected to publish as many papers as possible, etc., and at regular intervals, you will have to officially apply for a higher position. If your achievements are considered enough as a postdoc, you will get a tenure-track position, which will give you a maximum of 6 years to re-apply for a fully tenured position. If your performance is deemed insufficient, your contract will not be renewed, and you must head elsewhere.
Note that, after you sign your contract, your job title will only say something like "pre-hired teacher" or "pre-hired post-doc", which is a meaningless title. In many universities, after you sign the contract, you actually need to make a formal paper application in order to obtain an official job title such as "Assistant Professor".
Because the population of China is shrinking and money is dwindling, the whole application process is brutally competitive: in a single application season, I have seen as many as 600-650 applicants for approximately 10-15 tenure-track positions. 99% of these applicants are mainland Chinese, many of whom are quite well-prepared. If you do not have any papers published in Web of Science journals, you will have a very hard time being accepted in a top Chinese university, even as a post-doc.
Now, your mileage may vary, and I don't pretend to claim that my experience is valid for all the hundreds of universities in China, but here are some words of advice nevertheless.
If I were you, I would stay well clear of any up-and-coming university, and only focus on the top 5 universities of China in the cities of Beijing and Shanghai (especially since you mention you are from a R1 institution). There are numerous agents and representatives from up-and-coming universities very eager to hire you, but you will quickly find that many of their promises in terms of job conditions and salary treatment are empty or very misleading. The only exception I would make is if you already have a well-placed connection working in one of those universities, who can look after your back and fight to get you the proper conditions you were supposed to get. Representatives might show you nice photos of a clean university apartment, until you realize that place is in a newly-built campus in cheap land located in the middle of nowhere, and you actually need to take a crowded bus for 90 minutes (one way trip) to get to your actual workplace. It is these kind of things that you must take special care to watch out for.
My advice is for you to aim for a top institution that already has a few tenured foreign faculty in their ranks. Believe me, you do not want to be the first foreign hire of a given department. You will waste days and weeks running around various campuses and through the various administrative offices of the city, facing an army of clueless staff who have no clear idea how to process your paperwork as a foreigner. They will call lots of different people, and you might have to return to the same place 2 or 3 times because what a certain staff thought was the correct way to submit the application was actually incorrect, and you will need to rewrite the whole thing.
Since Chinese universities are leaner on administrative staff compared to the USA, you will likely be assisted in your paperwork by lots of different students who will go with you to the various offices around the city. They are wonderful, hard-working kids who are eager to work and learn from foreign faculty, but you will feel sorry for them taking so much time from their own studies to help get you registered, get a bank account, etc.
If you go to a large international city such as Shanghai, and if you choose a top university that already has foreign faculty, then it is much more likely that they already have some form of pipeline to handle your procedures, because practically none of the official paperwork you will have to do in China has any (decent) English translation. Until you master the Chinese language, you will be severely dependent on the aid of students and other faculty.
Another advice is to actually send an email to the foreign faculty in that department to get a clearer picture of the actual work/life conditions there. If you are lucky, one of these professors might offer some actual support for your candidacy, and look after your back while you are there. If you don't have friendly connections that you can trust, life in China can be very isolating and lonely.
Be sure to save as much money as possible before applying. In my case, because of the ridiculous amounts of bureaucracy and paperwork involved, it happened that I had to make a "work" visa to go to China and sign a temporary contract, and then leave the country to reapply for an actual visa that gives you not just a work permit, but also an official residence permit. Once you return to China, then you will sign the actual final contract. Unless the country's rules have changed recently, the same situation is likely to happen to you (be sure to inform yourself about this in advance). Also, because the paperwork for opening a bank account and actually getting paid is so cumbersome, it can take as much as 3-4 months until you actually start receiving a salary.
Finally, you will have to navigate the politics of your new country. You will likely be expected to sign a declaration of ethics, which along with traditional promises of not engaging in falsified research, you will have to check a box where you state that you agree and comply with the Party Chairman's vision for education in the country. There are lots of unwritten rules about what kind of research is "safe" to do, or whether you need to ask special permission to publish a paper that uses a certain dataset, but for the most part your Chinese/foreign colleagues will help you to understand what is safe or not, and as long as you are cautious and follow their counsel, you will probably find that there is very little (if any) intrusion in your research/teaching activities.
If you use your time wisely in China, and spend it on:
- working your ass off to get papers published in Web of Science
journals with high impact factors;
- getting a basic, working understanding of the Chinese language;
- applying for a successful government funding of your research;
- helping your Chinese colleagues and students to get their papers
published as well in good venues;
Then you will find that you can rise in your career much faster than in the USA (at least twice the speed, if not more).
However, if you are the kind of person who gets homesick easily, or cannot adapt to the culture or food, or cannot deal with being by yourself for long periods, or tend to spend your time in parties with alcohol (you will probably get lots of invitations, be wise about avoiding them as much as possible), you will probably have a dreadful experience. It's all up to you.
I don't really wish to go any deeper than this, and I hope others can give advice that is specifically suited to your needs. Good luck in your career.