There are two facts to know about controllers on Wii U VC. The first is that if you have a Pro Controller/Classic Controller connected to your Wii U, you're able to control the game using that controller AND the gamepad, simultaneously.
By which I mean: if you press a button on either controller, it will be sent to the game. For the control stick, the Pro/Classic controller takes precedence over the Gamepad controller stick.... but the gamepad stick is used if the pro/classic controller stick is in the neutral position.