How understanding are American Top-10 universities of different expectations abroad? In the UK, nearly nobody publishes anything before they start their PhD. The master courses are much shorter and usually include mostly courses instead of research. We are not expected to do any teaching. I am therefore wondering whether all of this will count against a UK student applying to the US. Personally, I have a very good profile for a UK student (Top of my class in undergrad and masters), but I only have 2 research internships outside of my courses. Is it expected of UK students to achieve the same things as US students applying to the same universities?
This may vary by field; my experience is in mathematics.
Most US students start a PhD program immediately after finishing their bachelor's degree, so they apply during the last year of their undergraduate program. It is less common to complete a separate master's first, especially in the sciences where PhD students are funded and masters students are typically not. The first couple of years of a PhD program are usually coursework similar to a masters program (you would probably be able to skip some or most of these courses, if they are comparable to what you have taken).
Therefore, the US students with whom you are competing are mainly undergraduates in the last year of their bachelors program. At this level a few of them may have published papers, but most will not. They may have research experience from summer projects, summer internships, independent study or lab work, but it is not usually comparable to graduate research. Very few of them will have any formal teaching experience; at most they may have worked as teaching assistants, which usually means grading homework. Some of them may have taken a few graduate-level courses at their undergraduate university, but not to the full extent of a masters degree.
So I don't think you need to be concerned about your level of preparation or experience in comparison with US applicants. If anything, you should be ahead.
As mentioned in comments, at a major US research department there should be people who have either come from UK universities or have experience with them. If they are not already on the graduate admissions committee, the committee members will consult with them if they have questions.
If you are literally talking Top-10, you will be on equal footing with American applicants, especially with your research internships.
Below that threshold you may well surpass American applicants, as you haven't spent any of your time minoring in side subjects since school.
This may not relate to how well your applications fare, but the larger universities will be well versed in taking on Eurasian applications, and you should expect fair judgement on UKish criteria.