What does formally means "putting under double check"?

I'm writing bot for FFA, and I can't understand what is the condition for double check and how exactly does the site calculate points for double and triple checks.

For example, if player 1 already was under check and then I check both players 1 and 2, then system also scores me 1 point.

That's not all.

1. two players could already both be checked the move before (so they are not putted under check by you). System also scores 1 point.

2. you can put them under check with not your pieces attacking. System also scores 1 point.

What is exact rule?

So, how to determine that MY move delivers check?

For example, if I checked Players 1 and 2 and also Player 3 was already under check, system doesn't score me 5 points (just 1!).