What about extra 20% of services as property taxes go up?

The May edition of the Messenger contained quotes from city council members implying higher property values raise property taxes. Please follow up to clarify. It is my understanding that the budget determines the amount collected, property values determine how those taxes are shared. To illustrate: if every property value doubled, the city would halve the tax rate – not double spending. This puts the council is in charge, not the assessor, and its members are free to stabilize our tax burden.
The city budget rose 42% from 2014 to 2022 while inflation was about 22%. I hope the council members can point out the extra 20% of services we're receiving.
Reed Mitchell
Longfellow