We got official confirmation that what you should actually do is to select the cards you are going to flip for the single effect, then flip them.
So no, it does not go back into the selection if you are told to flip multiple cards.
For example, if you have one face-down card and you are told to flip 3, you flip and resolve your one card once. You do not flip it three times, like you would if it were going back into the pool immediately.
I take it you are supposed to shuffle the face down horror before you start to flip them?
Otherwise you might keep selecting "minor shock" if you could remember where you flipped it last time.