On my iPad 4 an initial tap triggers the tooltip popover. A second tap seems to trigger the image swap. Desktop browsers won't produce any problems because your tooltips appear on hover. As you know, Its the click that then triggers the image swap. Since you can't hover on Apple touch devices that initial tap will trigger the tooltip first and require you to do a second tap to fire the image swap.
Its quite possible to hide the tooltip functionality on touch devices. From a usability standpoint this wouldn't be that bad since the image names appear below the large images anyway. Just a thought.