That's almost never a worry that plays out. Property taxes are usually a levy, allocated prorata based on total assessed value.

If your taxes are going up dramatically as values rise, that's either a sign of issues with equalization rates (the county/town/city needs to periodically reassess), or that other areas in the jurisdiction are declining relative to value. You often see that in cities where property values often mirrors the old "redline" maps... gentrification gets you million dollar condos, but two blocks away some tenement is declining in relative value.