As far as I have seen, in practice there is almost no real recourse for taxpayers to stop a taxing jurisdiction from grabbing up to 8% in yearly increases when values rise, whether due to apathy, or lack of information, etc.
An exception to this is Houston, where the city charter was amended to cap the revenue increase that the city of Houston is allowed to collect from property taxes. In the three years since I have owned my condo, for example, my value has gone up by 21%, but my tax bill to the city of Houston has only gone up 12% because the city charter now limits them to only raising their property tax revenues by 4.5% max per year and so the city tax rate is forced to decline every year when values go up.