The rings are in jumping just before an enemy touches you. If you time it right you don't have to jump "on" them. Although sometimes this will throw you into an unavoidable collision.
I'd suggest adding a state transition on sonic that only let's the character destroy enemies when coming down from the peak of the jump. Or else make it a double click to be able to destroy enemies from take off as a special trick move.
The parallax effect on the vertical axis doesn't really make sense in terms of perspective.. the camera isn't travelling up, just the character.... and even then, depending on the distance it probably wouldn't be pronounced like it is here. It's a nice effect but I think the game would be fine if it was a horizontal parallax instead or non at all.
Good job! Great game, fun.
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