Does anyone know what the Fide rules are for when you are allowed to move OTB

According to FIDE laws you may actually move once your opponent has MADE his move, but he must still be allowed to complete it by pressing his clock.

Thus the following sequence is legitimate (and regularily seen especially in Blitz games):
- A moves
- B moves
- A presses clock to complete his previous move
- B presses clock to complete his previous move

A move may only be taken back if it conflicts with the basic rules. (e.g. leaving own king in check)
And even still, the alternate move must be according to "touch move rule" if that is possible.

There may be different or even contradicting laws for games under USCF or other non-FIDE-conform rule-sets.

The way it worked was

A moves
A moves
I remind him he made 2 moves at once.
Reset position
A hits clock
B moves
B resigns a few moves later.

I was b