What is measured
The signal is drawn in the next screen frame, and the clock starts at the timestamp of that frame: the moment the change was handed to the display. Your tap is timed by the input event itself (the moment the browser received the press), not by when the page got round to handling it. The difference between the two is your time for that trial.
Five valid taps are averaged into the result. Beside the average the card gives the median, which shrugs off one slow tap, and your quickest tap of the run.
False starts
Tapping before the signal is a false start, and so is tapping within 100 ms of it: no one can answer a visual signal that fast, so such a tap was already on its way before the signal appeared. Either way the trial is run again after a new random wait, and the result card keeps count of your false starts.
What the browser cannot see
Between the frame and your eyes there is the display's own delay, and between your finger and the browser there is the delay of the touchscreen, mouse or keyboard. These vary between devices by tens of milliseconds and are part of every time you see.
So a time is a fair comparison only with other times on the same device. If you play on a phone and a laptop, keep two sets of expectations.
Comparing runs fairly
Look at the chart on the result card rather than at one run. A single tap can be slow for reasons that have nothing to do with you, and five taps are a small sample.
On the Reaction Time ladder each step fixes the waits before the signals, so two attempts at the same step are as close to the same test as the game can make them.