If your test is scheduled with a commercial lab that caters to COVID travel screening, the 24 hours is guaranteed. I did mine at such a lab (not on west coast), and I got my result within guaranteed timeline.
I submitted my test on Sunday afternoon, and I received pre-approval 30 minutes later.
Depending on your flight arrangement, if both stops are on the same itinerary, you probably would need SXM pre-approval to board the first leg. Maybe a bit more time buffer before your first leg would be helpful, just in case.