Development kits come with software on the module. Buying just a module comes with a blank module in need of flash. Obviously, if the module is blank, then it won’t work on the alternate carrier board, but if the module came from a dev kit with software, then the board support package will be wrong for the alternate carrier board. The only way this would work out of the box is if the module was flashed with the board support package for that specific carrier board. Did Colorado Engineering sell the carrier board with the module and have it flashed for that alternate carrier board? If not, then you have to flash (you’d use the flashing software provided by NVIDIA, but you’d need to first apply Colorado Engineering’s BSP).
Btw, the device tree is the major difference among carrier board BSPs. The device tree changes the way various pins and functions are routed to the carrier board from the module. Even if the HDMI worked it would be very likely a large number of other functions would not work (unless their carrier board is electrically an exact duplicate of the dev kit carrier board).