I get the same pain in my palm, though I don't feel a tendon shifting or anything. It's more like I have a cut under my skin or like a vein pinching. I just have to re-adjust my grip to put more of the weight on the inside base of my palms when benching. Play around with your thumb positioning and allow your body to adjust accordingly to what you're putting it through. Oh and make sure your wrist is straight, I have a bad habit of not keeping my wrists straight all the time!