putting aside that the air is currently fine in CM, apologies, I misread what you said. The inverse is true. If you're living in Phuket, not CM, you should get the car and bikes registered there. You should have plates reflecting where you live.
If you don't mind me asking - why Phuket? I can understand why you'd hate March in CM but it's not a place I'd move to down south given a choice. Everything is twice as expensive and the locals aren't nearly as nice.