Well, for the win category it says that the timer starts when the game resets and for the kill category it's on first movement. I'm sorry, but what do you mean by first explosion @Grump ?

Not really a real category, just really as a RNG joke. Just destroy any tower and that's it.

The timer starts when the game restarts and ends when it says that you eleminated the team you were aiming for (unless the players get removed from the leaderboard before it says that you eleminated them).

Let me know what you think.

So what they mean by the first input is when you lets say press W (forward). In short, when you start moving, the timer starts. Of course, it depends on what category you mean.