I would not presume that 'should' will translate to 'will' without other evidence, especially when my printed warranty includes the additional condition that the vehicle be sold in a California emissions state. It is theoretically possible that the original price structure in CA (not necessarily visible to the consumer) includes some provision to pay for the longer warranty. The VIN will connect them to all necessary records.
That's good advice on making the appointment except you were too optimistic. I just tried to make an appointment in the Sacramento area and the soonest I could make an appointment was nearly 2 months. If you can't make an appointment do a walk-in at a small town DMV near where you live and go mid-week.
I believe it is where the car was FIRST PURCHASED and first REGISTERED that creates the warranty obligation from Toyota (otherwise all the +100k Prius with dead batteries would get shipped to CA for free repairs). Currently getting $3k battery reimbursed to relative who had car fixed on a road trip outside of CA. Pretty miffed at dealer, as the state it was in IS a CA carb state and they should have known better that to charge her at 106k on a CA vehicle takes them under 1 min to look up VIN. They aren't fighting it though.