I applied for a tenure-track assistant professor position in the US, was selected as a semi-finalist and had my first round of interview. The next step is that they will choose around three finalists to be invited for an on-campus interview. Does anyone have an idea how long it would take to be notified after the first-round interview in case one is selected as finalist? Thanks!
The department will be assembling all input from anybody who has anything to say about the visiting applicants. From there, probably a committee will meet and try to make decisions about who the "finalists" are, or possibly, the chair may decide alone. Tentative choices may or may not need to be preapproved by a dean.
My suspicion is that much of this is probably handled within two weeks to a month, maybe six weeks. Since faculty slots are so competitive, nobody wants to lose a top candidate because they're moving too slowly.
The candidates who don't make the final list may not be notified of that until a candidate signs a contract of employment, or maybe even never.
Frankly, I feel that department probably overshared about their process. At many private universities, this process is not carved in stone, and could change (though for some public institutions, the process may be proscribed in code). For example, let's say after the first round, the whole faculty agrees that one candidate clearly floated to the top. There's really nothing keeping that department from starting the brass tacks discussions with that candidate, and not inviting anyone else if it looks like the candidate may accept the job. In fact, I'd say there are real incentives to doing so.
The bottom line is that you shouldn't let their description of their process change your process at all. You interviewed, and you gave it your best shot. Now, if you're serious about finding a job, you simply keep looking and keep interviewing, not worrying about whether you're going to be a finalist in some school's process. If they invite you, or even if they offer you a position, continuing to interview might put you in a better negotiating position, or some options about which job you accept.
That would depend entirely on the process, your place in the line, and how strictly rules are followed. For example, if someone else and you are selected for final candidacy, but they still need a third finalist which they could not identify in the current set of interviewees, the time might be quite long. Another example would be that you did not make it into the group of three, but are the runner-up. If they have a strict process, they will not tell you no because they still might want invite you, but of course they cannot invite you now. If you are applying from abroad, certain rules need to be followed in order to extend you an invitation, which could further delay the process.
On the other hand, you might have already received an invitation by now.
If you are given an offer by someone else, then you have ample reason to contact them about the timing.