There is a necessary time interval between when you see something and when you do anything about it. The information has to pass from your eyes to your brain and from your brain to your fingers, and of course it takes a little while for your brain to process the information. The time interval is about a quarter of a second, though it varies a lot from person to person, and with the kind of signal that is given and the kind of response you are going to make.
A classic way to demonstrate the reaction time is for one person to drop a ruler (held vertically) that is passing through another person's fingers; they are supposed to stop the fall by closing their hand. The distance that the ruler has fallen gives a measure of the reaction time.
Since it only takes about 1/2 second for a coin to fall from eye level to the floor, reaction time will be a serious complication in timing. For example, if the person operating the timer is watching as someone else drops the coin, he will almost surely start the timer a quarter-second late; if the person with the timer is listening for the coin to hit the floor, the timer will likely stop the timer about a quarter second late, too. So possibly the measured value is right -- but it is clearly hard to guarantee this.
An alternative is to have the person with the timer be able to anticipate the drop of the coin (by saying "ready ... set ... go" and to watch the coin and anticipate its hitting the floor. The reaction time delays are still present, but we have all learned to compensate for them (or no one would be able to play ping-pong at all). Readings made this way are more likely to be consistent and more nearly correct.
Here is a timer that lets you anticipate the start