A lot of people seem to think that the property tax is set at a certain percentage, and if property values rise, the government just dances around in a fountain of dollar bills.
Everywhere I've looked, it's as you say: the local government sets a budget first, then that year's property tax rate is set at a level which brings in that much money.
There is a somewhat delayed and simplified version of what people think there is - as property values climb, the city will notice and budget more (or less if severe drops) and try to stay within some standard percentage.
Everywhere I've looked, it's as you say: the local government sets a budget first, then that year's property tax rate is set at a level which brings in that much money.