What time scale is typical for the evaluation of applications for an assistant professorship in Japan?
It depends on the position, but couple of month is a reasonable scale. If you go through the first round (your resume is picked, which itself easily a month), you are contacted for an interview generally at least a month before the interview. However I have seen cases when it took months just to appoint an interview.
Note that many assistant professors are getting jobs by internal promotions and not through public advertisement.