My comment on domestic connections is only pertinent to MEX Terminal 2 - I have no idea if T1 is the same. Sorry for the confusion.

For USA-MEX-PVR or PVR-MEX-USA. As described before (at least regarding Terminal 2.)
For MEX-PVR-USA. I would treat it as two completely separate flights. As in when you arrive PVR from MEX, leave baggage claim, you need to start the check-in process with Alaska for your USA flight, go though security, go through US screening (easy, usual questions) and on your USA bound flight.
For USA-PVR-MEX. Again, separate flights. Arriving PVR, immigration and customs, leave customs to do check in on budget airline to MEX, go through security.

A PVR expert needs to weigh in on what wait times would be like for check in/security look like to determine if 1 hour is enough.