A prop while turning is trying to move forward and also trying to climb out of the water. The prop rotates clockwise, so when your turning left it has an easier time getting to the surface, and more so the tighter turn you make. Most boats need to have the trim moved in a bit on tight turns. If your pulling a tube, just keep the trim in a bit more then for just cruising.
What kind of Mark Twain? I had a '76 180T and loved it. Just took too much of my time maintaining it. By the way, it had an anti-cavitation plate and I never had that issue.