You don't do 90 day reports on a covid extension, period. There is no "up to immigration office." 90 day reports are for people who's visas or extensions are longer than 90 days.
You don't need to do the 90 day reports then if you're in Phuket, Bangkok, or chiang mai. The elite people do the for you, you just need to give them your passport.
Per your visa or extension. If you leave the country and come back with a new visa, the process starts over again. After your first yearly extension you shouldn't have to come in person again if you keep that extension active.