TDS meters measure the conductivity of the water, which can help identify salts or other impurities which have positive charges. However, common disinfection by-products in water, such as chlorine, iron, chloramine etc, do not impact the conductivity of the water. So they would not be picked up by a TDS meter.
So for measuring general water quality, a TDS meter is not very helpful. Instead, it would be better to use more specialized tests to test for specific chemicals or metals, such as a chlorine colorimeter.