Why does wand shower head drain at unusual times?
If I had to guess, it's draining some of the water that was still caught up in the shower head after you turned it off (and held there by atmospheric pressure). After enough of the remaining water has evaporated/etc to break the seal, the rest of the water comes out. We have a similar problem with our shower head (a flat "rain" shower head on an articulated arm). In our case the problem is depends on the position of the head and arm...oddly enough it happens when the head is not horizontal. All the other details are the same as yours (it never happened with the old head, no lower faucet, etc).

In our case it's not draining 1-2 cups since it sure sounds like it at 3AM in the morning and scared my wife on many occasions :-). You could verify the amount of drainage by putting a pan or something in the shower...if yours is indeed draining 1-2 cups it may not be the same issue unless it's somehow siphoning water out of the hose.