My son was taught to relax the glove during the delivery. About the time when the pitcher is starting to move to the plate, the hand relaxes and the glove closes slightly. Some catchers relax the wrist, making the glove drop, but my son prefers a subtler move in which the hand closes a bit as the pitch is on its way.
The reason to do this is because a relaxed hand is quicker to the ball, and softer on the catch.
Looking at your son's man on stance, it is a little hard to tell, but it seems to me his feet should be wider, butt higher, and back more parallel to the ground.