The reverse effect is correct, this is the classic game interaction design challenge of 3rd person vehicle cameras which aren't pegged facing the forward direction of the vehicle.

Our hand-eye coordination does not intuitively adapt to remap the arrow keys relative to the spatial position/orientation of the vehicle, and we keep thinking relative to the screen coordinates itself. After you play with it for about 5 minutes you will project to the car instead of the screen and it will feel intuitive again.