Are cheaters using bots in 'puzzle battle'?

The way puzzle battle starts at my device is, there is a 3 second countdown after search. On the second to last or the last second it's mentioned whose move it is, and immediately after the countdown, the move of the puzzle is made. I have seen many times that almost .1 or .2 second after the 'puzzle move', the player has solved the puzzle! 

Are such players using bots? If not how is this possible online?

I can accept that people can be amazingly fast thinkers, but to click and move the mouse around the minimum time required is .8 second or so. 

Can anyone please explain how are they solving so super fast?

i have a touchscreen computer so moving that fast isnt out of the question, and i can think during the countdown.