They have to be swapped somewhere.Are the wires swapped in error in the either trailer side plug or the harness side plug? Appears the wires coming into and out of the module are correct color codes for left and right turn (left yellow/right green).
Do you have a wiring diagram of the trailer side ?
I assume that the square connectors have a "key" for proper alignment ?
Was the input connector for the module already on the bike......or did you install that too ??
The transposition could be all the way back there.