When to call catcher's interferance?

[voiceoflg]

Completely pleading ignorance (now that it's been several hours and I've cooled off). Please educate me.

R1, one out, tie game, FED. Batter hits into a 6-4-3 DP to end the inning...or so it seemed. After the DP was turned and as the players are coming off the field, PU calls time and puts everyone back saying catcher's interference, that the bat clipped the mitt. Batter then gets back in the box and hits a double down the line on the next pitch scoring the runner from first.

Fans on one side was livid that catcher's interference was not called immediately, and a few fans for the other team told me they also disagreed with the call, but they'd take it.

So when is CI supposed to be called? Immediately as it happened or after the play? I was unsure and the folks back home are probably mad at me for not berating the ump on the air for waiting, but I said I was not sure when it is supposed to be called, saying if the result of the play that the CI happened was a base hit, there was no advantage and it wouldn't have mattered. But since there was an advantage with the DP, it probably had to be called then.

What say you?