I have had this same problem almost every time that I've used Tandy rivets. Personally, I think that their rivets are just of inferior quality. They don't seem to mushroom out or split properly. In my experience, only about 30 out of 100 will function as intended, and that was only when I used a pair of jeweler wire-cutters to pre-split them. You should be using a rivet setter base, though. It helps keep the post from flattening and looking janky. It also keeps the post from sliding around and giving the bend you're getting.
My suggestion are 'screw rivets' or Chicago screws. There are also other rivet makers that are better, such as Hanson Rivets. However, the screw rivets are changeable if they become damaged over time. They aren't that much more expensive than regular tap rivets, either.
-Crystal