In terms of "rubbing the fingers together, then producing a coin", I suspect they actually had the coin in some kind of Downs palm. I don't often do this, but I quite often put the coin into a Down's palm finger clip... have the coin in finger palm, then bring the index finger over the coin and use it to pinch the coin between index and middle finger, somewhere between the two finger joints. You should be able to straighten your hand and the coin will be clipped between these two fingers, sticking out perpendicular to the hand. Obviously, you wouldn't do this, you'd keep the hand naturally curled - the coin is now in a sort of Down's palm position, only it's being supported by the clip of the fingers, not by the thumb.
You can now put your thumb under the coin, and push sharply up (almost is if you were flipping a coin). As you do so, you pinch the coin between the middle of your index finger and your thumb. The bottom edge pops off the middle finger and thus out of the finger clip. This "flips" the coin into view, which is much more visual than pushing it into view from a finger palm.
Hope that made some sense! I'd do a video but I can't find the lead for my camera
Edit: this is especially good for producing a coin "from the mouth" because as you push the coin up with the thumb, you sort of flip it into your mouth, so when it is revealed it is actually half in your mouth and you are seen to pull it out.