The most common problem was the door key cylinder switch staying open due to corrosion. Try it on the passenger side (if there is a passenger side key lock).
If the module doesn't see a turn of the key cylinder switch to disarm the system before the dome light comes on, it would be the same as the door lock being jimmied to open the door and setting off the alarm.
I believe that the FOB unlock also mechanically actuates the key cyl. switch linkage for the unlock signal.