This is a very common occurance in young children, and sometimes in not-so-young students. I don't dwell on it throughout the lesson, but I do demonstrate and explain to beginner students (as needed during the first few months of lessons) how the fingers SHOULD look compared to what their fingers ARE doing. I tell them that it is quite common for new students' fingers to fly up like that, (I don't want them to think they have a rare problem) but that with careful attention to their fingers in their warmup exercises, their fingers will begin cooperating better. (I don't focus too much on flying fingers during the student's playing of a piece, because they are so focused on notes, rhythm, touch, etc that one more thing is just too much).
For warmups, I have them place one hand on 5 white keys, with an imaginary "bubble" under it to form the proper curve. I'll have the student play just ONE note repeatedly, (with the same finger of course), while watching for flying fingers. They are not to repeat the note until all fingers have rested back down on the keys in a nice curve. They are to repeat this exercise with all 10 fingers, until (after a period of months) they can fairly well eliminate the flying fingers. Warmups also include very slow 5-note patterns (ie CDEFG) with every finger resting on keys; if one "pops up" he must bring it back down before playing the next note.
These are exercises that can be done on a tabletop or on one's thigh while sitting in a chair or car, so the student can gets lots of finger practice during the week.
It sounds pretty basic but it really does help.
Topic: Flapping fingers!