I suspect that the pads aren't rotating, but the brake arms are flexing forward raising the front end of the shoes (pads).

Step one is to either grab the arms and wiggle them to see if there's any play. There shouldn't be any except a trace so they don't bind at the pivots. Once you do that you'll still have some flex (not free play) When you apply the brakes the motion of the rim pushers the arm forward, and that will cause the shoes to rise somewhat. Mount the shoes a bit lower to compensate for the flex, and check your work by applying the brake and pushing the bike forward causing maximum arm flex.