Checkmate and Clock rule?

If that is the case then the arbiter made the right call because black had insufficient mating material.

I played in a USCF rated blitz tournament yesterday and a dispute came up on another board. None of us, including the TD knew the rule.
White had 2 seconds on the clock. He delivered mate before the clock ran out but pushed the button just after it hit 0:00.
My feeling is that mate in the board is the end of the game but what is the actual rule?
The game was called a draw since nobody knew.

Q:What's a chess clock and how do they work? A:A chess clock is actually two clocks! When you're thinking, your clock ticks down. After making a move, you hit a button at the top of the clock and your opponent's clock starts ticking. If you run out of time, you lose the game, unless there is checkmate on the board or your opponent has insufficient mating material. There are two main types, the digital and analog clock. that is taken from the faq page on uscf website

White had 2 seconds on the clock. He delivered mate before the clock ran out but pushed the button just after it hit 0:00.
My feeling is that mate in the board is the end of the game but what is the actual rule?
The game was called a draw since nobody knew.