clifford matrix rsIII false alarm problem

your right with the optional dome light supervision wire it is not needed in your sercumstance.

The next thing i would do is to make sure you have not accidently connected the violet door trigger wire instead of the green, i say this because if you have, the alarm will work in reverse so you will be able to arm the alarm with the door open and it will bypass chirp with the door closed. 

I would also see how the car responds to not using the alarm e.g. what happens to the dome light when the doors are locked with the key, does the dome fade out immediatly or does it take 30 seconds to fade out, if the light fades immediatly when locked with the key and doesn't when the alarm locks the doors then i would look for different locking wires which will fade the light when the alarm arms.

also maybe try a different door wire most dome lights only have a single wire that runs up the a pillar or b pillar which may help your problem, cause your not using two circuits on the one wire you can test this by removing the dome light and testing the wire directly at the light, using a test light the bulb will come on when the door is closed and go off when the door is open check each door individualy to see if this wire is the one you are looking for, remember, because the dome light fades you may have to wait for the test light to light up after the door is closed.

Again haven't worked on the car so i'm just guessing to what i would try if it was here also try only connecting one dome light wire instead of both and see if you can issolate the problem to just one circuit good luck hope this helps let me know what you find