How to use a Bluetooth-controlled relay to simulate a button press on a garage door remote?
The module contains two relays, each having normally open and normally closed pins.
If you want to do it the simple way, you can disassemble your garage remote and solder wires to the buttons, then connect them to the normally open pins of one of the relays. (I actually did this soldering thing to my garage remote, it's not super pretty but it's been working for a few years)
As long as you can verify that the designed input voltage of the module is indeed 12 volts and you can be sure that the 12V supply is good, I don't see any issues with it.