Chlorine is among the top 10 highest level of production chemicals in the U.S. As a bleaching and cleaning agent, it does wonders in keeping your pool water clear and sparkling clean, but the same characteristics don't work so well when it comes into contact with living plants. In small doses, chlorine will simply singe a shrub, though larger doses can certainly kill. Luckily chlorine from pool runoff doesn't appear to cause long-term damage to the soil, allowing for replanting.
The effects of swimming pool water draining onto your lawn, trees, shrubs, or grass can be intensified by environmental factors like temperature, especially if the sun is shining brightly and the thermometer is heading upwards. A hot, sunny day can magnify the damage chlorine does to living shrubs or trees, perhaps even turning a simple singe into an all-out burn. One way to avoid the problem is to schedule pool draining or cleaning for cloudy days or at night.
Water drainage that contains a more diluted form of chlorine has less potential to hurt your lawn. Conversely, highly concentrated pool chemicals and additives hold the greatest chance for creating havoc. Thus holding off on pool draining until the chemicals placed into the pool have had ample time to become diluted makes sense and could make the difference between a "non event" pool draining or a widespread flora massacre.
One approach to the problem of pool chemical collateral damage is to plan ahead and install some sort of drainage system that funnels water away from trees, shrubs, and grass, which should help reduce the amount of chemical burn that occurs. As far as random splashing from swimming pool users, if you notice that the water is becoming a problem to your yard, install some sort of protective barrier around the pool, such as a wooden deck or concrete pad.