So basically I just need to switch around one of the cables.

Not necessarily. That might or might not be your problem. We can't know without someone opening up your dash and checking it.

It's possible that the tuner module is genuinely faulty. It's also possible that it's some other wiring problem, either something CarToys did wrong, or perhaps it's this problem. Someone with experience and a good eye needs to look at the installation closely and carefully to determine where the fault is.