You should not use the indexed functions for this (GetPlayerPawn / Character). In a multiplayer setup you’d have trouble getting the correct index. In singleplayer, AI characters for example wouldn’t want to reference players anyways. Instead, stick to the references already available (TryGetPawnOwner) and cast, GetController from there if you need it… This is also why the puppet effect happens, as all the AnimBPs get their data from the same pawn (which is not what you want usually).
I am now not quite sure… which character is it you want to animate? If it’s the MyCharacter, you also need to cast to MyCharacter. A cast to ThirdPersonCharacter will always fail (except if MyCharacter is a child BP of TPC).