The concentration of fluoride and chlorine in normal municipal water supplies is not sufficient to cause damage to your plants. However, hard water can do damage. Letting hard water sit out in the open simply concentrates the mineral salts as the water evaporates. If your tap water is hard, use filtered, distilled or rainwater. It may also help to flush lots of clear water through the soil to wash any soil salts that may have built up.
Letting the soil get too dry also causes the mineral salts to concentrate and burn the roots, so be very careful not to let the soil get too dry. It is also important to always water thoroughly so that a bit trickles through the drain hole each time. Partial watering will also concentrate mineral salts where the water penetration stops.
The leaf in the second photo looks like it might be spider mite damage. Probably not, but check and remove that leaf in any case. Other brown tips can be trimmed off.
As long as the newer leaves remain healthy, then your Ti Plant should be fine.