What your score includes
The time runs from the moment the browser hands the green frame to your screen until your click arrives. That includes your reaction, but also your screen's refresh delay and your mouse or touchscreen's input delay — together often a few tens of milliseconds. A fast gaming monitor and wired mouse will score better than a phone, with the same person.
Most people react to a simple visual signal in roughly a fifth to a quarter of a second. Fatigue, distraction and caffeine all move the number; compare yourself on the same device rather than against someone else's.
Questions
What is a good reaction time?
For a simple click-on-green test, most people land somewhere around 200 to 300 milliseconds. Your device's display and input delay are included, so compare scores on the same device.
Why did it say too soon?
You clicked before the screen turned green. The wait is random so the change can't be anticipated.
Can I use the keyboard?
Yes — press Space or Enter instead of clicking.