I haven't myself got to the point where I'm teaching Apollo tricks like these. I have noticed a difference in behaviour when it comes to training and playing.
When playing, which is normally on my shoulder when I'm giving him pats, he will flip over and hold on to my finger then continue to nibble on things around him. He will not however let go of my finger and if he does, he will immediately flip over just like you explain.
Recently I've been doing some taming training, giving him peanuts for letting me touch his beak, back, wings, etc.
This was a process over a few days where at first I had to get him used to my cupped hand being near him. Then I moved on to touching his back for progressively longer times. Then once he was okay with that I started to put some pressure on his wings as if I was going to pick him up. Then now he is at the point where I can grab him around the wings and flip him on his back for a few seconds before he wants to get back up. Afterward each time, of course, he gets peanuts for being good
I was trying to follow the same method from Michael's video with Truman
http://www.youtube.com/watch?v=eNGOyeLjxhI&list=PLAC3C0A2495F6E11F where he was getting him used to a towel.
Hope this helps.