Well, if there is no wire on the back of the head unit for reverse and it's auto sensing, then it sounds correctly wired. As far as the rear view in that you say is audio, I'm assuming you mean an rca jack that is the video input for the camera. Once the camera has power, it will send video. Can you upload pictures of the wiring diagrams for the camera and head unit? I could guide you better with those.
EDIT: I found the wiring for the head unit. Do you have the purple wire on pin 3 of the head unit wiring harness? If so, that need to be hooked to the reverse wire as well. That sends the signal to let the head unit know you are in reverse and display the video input from the back up cam.