No, that is not necessarily true. The amount of the exemptions that are granted by each taxing entity is subtracted from the market value of your residence and the taxes are calculated on that "lower value". In addition, when you turn 65, your taxes for the school district in which you reside are frozen at the level established during the first year of qualification for the senior citizen exemption.
Some taxing jurisdictions other than school districts may also offer a tax ceiling. Call our office at (936) 327-2174 if you have any questions about this.