I've been testing on iPad and also Asus Transformer (Android platform) and neither work. I've set up other players for iPad and Android and the touch controls worked fine, so I thought it might be something in the setup. I removed as many things as I could without success. I am using autohide, but removing that option didn't change anything. I am also using SVGs for the player control displays, and I took those out too, as well as the touch events that add a colored shadow to the button on touchstart. I thought it might be something related to the styles. For example, for this player there are controls both top and bottom, so the jp-interface itself has no actual dimension, with the top and bottom controls being absolutely positioned and having their own dimension. This is so the interface doesn't cover up the entire video element. I was hoping someone else may have experienced the same type of problem with touch controls and new how to correct it. Also, strangely enough, I do not have this problem in the standard browser of the Asus tablet, which happens to be Mozilla based.
From what you wrote, this might actually be a jQuery problem?