You cannot animate a layer's position, rotation, or scale when applying Puppet Pin. The Mesh does not follow the layer movement, so everything breaks. You must complete the puppet pin animation on the layer, then pre-compose or add the comp to a Master comp before you can animate the layer's position. This makes complex character animation difficult. The fingers would have to move independently of the rest of the hand (on a separate layer, then be pre-composed, then the hand and fingers combined in another comp and attached to an arm. If the aArm is also animated using a puppet pin, then the Arm and hand must be pre-composed and connected to the body so you can move it.
Puppet Pin is very handy for simple movements, but complex animations like fingers snappinwilld waving as your character is much more efficiently. Ifkly.
Character Animator or a 3D app like , I would explore those optionsBlender or C4D allows you to rig a character much more efficiently. I would explore those options if you have a lot of this kind of work to do.