MobileSafari as a rule has incorrect HTML button behavior (incorrect meaning: \"not like an iOS native button\"). Correct button behavior is as follows:
Basically what you'd want to do is build out some sort of hybrid hover functionality for touch devices, which detects when your finger moves in/out of the button in question.
I built a basic JSFiddle which implements some barebones functionality. If you know any javascript, I think you'll get the idea.
Live JSFiddle DEMO
Try it on your iOS device (and maybe your Android device??).
- brian