Dropped third strike, batter-runner kicks the ball

[Gre144]

I never seen this before. Dropped third strike and batter-runner accidently kicks the ball as he runs towards first base. It probably could be describe better by saying the ball landed in the pathway of the batter-runner as he headed towards first.

Coach screams at me that I should have called the batter-runner out immediately.

1)Could someone direct me to the Fed Rule that would describe how to hand this situation?

2)When is the batter runner considered to be out of the batter's box as he runs towards first? I think that where he is at the time he accidently contacts the ball plays an important part in determining if he is out or not.