That's odd. The way you actuate the doors doesn't involve cutting a circuit (like ignition kill). When wired correctly the alarm should trigger the cars stock relays behind the ECM.
I guess the first place to look would be the stock relays. If the installer back then was a hack, check the grommet running into the doors for any signs of wiring. A good installer won't show his tracks there, a hack will leave cuts or the wires on the outside of the loom.