So I understand you've failed to do anything proper with the module? Alright so I'll get right down to it, with the very simple basics just to get it working, I'm not a pro myself. Doing this out of my memory:
1. Spawn the module (I think near an airport you'd like to use), sync it to the Military AI Commander of that side. I never make the module spawn any AA, air assets etc. Never have I either messed with the ATO (TAORs) with this module, I don't find any need to. To the faction part I write the faction whose planes I'm using.
2. Personally I always hand-place the aircrafts that the module will use, so do this: Spawn an EMPTY aircraft of your choosing, place it down to the airport. Sync the plane to the Virtual Profile module, when it's set to "Profile synced.." as it is by default. Important: If that aircraft is from another faction, set your Air Component Module to that faction and also ADD THAT FACTION INTO THE MILITARY AI COMMANDER MODULE!
That'll do unless I forgot to add something. Turn the debug on, and start the game. If the airport has a flag on it, that means it's detecting that airport as the correct one. With the debug on you'll get notifications when there's a request for Air Components. When that happens, the plane will teleport to a location within the airport, alarm bell will go off and the pilots will run into the planes and take off.
The reason I don't mess with Responsibility Areas with this module is that the groups actually request for CAS etc, it's not random, it's requested by real events going on. And it's sweet. If you want to edit what type of orders the planes can do, I'd guess that removing the ones from the field that you don't desire will do the trick, but I don't see why you would do that.