Why did I win?

In this game, if I check in the study, it will say I have 0 sec left while the other guy has .4 secs left so why did I win on time

The time you see is the time at the start of the move. If your opponent then takes more than 0.4 seconds then they lose.

As for your own time, the 0.0 seconds you see is rounded, and you actually had 0.06 seconds. You can see this by going to the game and clicking move times below the board, and hovering over the specific moves.

Disclaimer: I am not a dev.

Ok thanks