The blueprint itself is a class, which you can instantiate as many times as you like. For example, if the class is “Human” you can spawn instances of humans in your world such as “Bob, Steve” etc. Meaning that when you spawn actor A and actor B, playing an animation on instance A does not trigger the animation on B. If it does, post a screenshot of your code here so we can check it out. If this info is new to you I recommend watching a tutorial on youtube about the difference between classes and instances.
This is a bit abstract. In a normal situation you have a PlayerController per player, which controls a character (Pawn) spawned from a blueprint. Both the playercontroller class and the pawn class are set on your GameMode class. Just by setting those classes on the gamemode the engine will already instantiate the pawn and controller for you.