the amount of time it takes sound to travel the distance from the gun (in the 100 and 200) to the finish line is relatively close to the average untrained reaction time.
So if reacting to seeing the smoke, you should end up starting the watch at about the same time you do hear the sound. Your timer probably was crap...in your favor! but good timers will use both the smoke and the sound to really lock in. At the very least, it meant the timers at our meets were pretty consistent among the lot. I could (humblebrag) pretty consistently beat the sound of the gun in the 100m, but it was more important to be consistent with everyone else.