I bought the Peak Pro/Carta 2 Spinner plug, what do I need for this to work on the Peak Pro?

So I bought the Peak Pro/Carta 2 Spinner Plug.

On the website it says “Fits Puffco Bubble Cap and Joystick Tether”…. So can I just remove the joystick from the cap and insert this plug? It looks bigger than the hole the joystick is in.

Do I need any other cap for this to work? Or is just this perfectly fine?

Thanks!