if a school is accepting applications for faculty through September 15, when does the job start?
Only the hiring institution knows for sure, so you would have to ask them.

However, the start date is almost always listed in the job posting, so to avoid looking silly, be sure to read the posting carefully, as well as any  accompanying information that is included or linked.  If you don't find it, then contact the hiring institution (the posting probably contains contact info for a responsible person).