Batter swinging at a pitch late

[Backjudge79]

I have noticed that there is an increasing trend of batters being coached at swinging very late at a pitch to protect a runner stealing a base at the high school level. Happened twice last night. My timing is pretty good for calling pitches, that is slow. The first time it happened I correctly called the pitch a strike. The second time it happened the swing was so late I had already called the pitch a ball then the batter swing his bat. There was no interference with the throw to second because of the late swing.

My solution to this was to call time after the play and ask my partner for help, which I knew he may not have any because he was turning to call the play at second. After giving him so very subtle hints, that I wanted him to say he swing, I was able to sell my reversal of a called ball without anyone objecting to it.

My question is this.

1) How late can a batter swing at a pitch without it being called a strike.
2) Did I handle this the best way under the circumstances.