Do I need to apply for my initial retirement visa in the same province where I plan to reside?

Yes

If you're going to get the initial 90 day non-O visa in Thailand, then you need to apply for it in the same place you will be applying for the first 1-year extension. No immigration office in Thailand will let you apply for the 1-year extension based off a 90-day non-O visa that was granted by a different immigration office.