Not sure about that in general, although it can differ for each state and could apply in your state. In general, US tax income from property taxes has not risen, in fact it's slightly come down as a percentage of income. That means that while the tax base (property values) have increased sharply, the tax rate for property has come down.
Most municipalities will first establish how much tax revenue they need, then look at the total property values that's taxable, and then set an appropriate rate. If property values double but municipal expenses don't, they can and do lower the property taxes. It's not a 1 on 1 relationship but given average property tax income as a percentage of total income has slightly come down over the past decades, it's clear that tax rates are being reduced as property values go up.