^agree. Sounds like the alarm doing the work. Some alarms are programmed to lock the car automatically. Not super familar with the alarm you have, but many that I've had will lock the doors in various situations depending on program function settings.
Example, remote the doors to unlock, if you don't open a door in 30 seconds or so the system locks the doors again and rearms.
When key is put in ignition and switched on the doors will lock, when switched off they will unlock etc.
Quick search for you and so far I've only found info that programs the remotes from the look of it. http://www.carkb.com/Uwe/Forum.aspx/...ing-and-manual
If you scan down the posts someone put the instructions on a couple of different posts. Could be useful.
I see a good number of posts saying these alarms were installed as part of a Gulf States deal. I did find what looks like a tech number that might help if still active (sorry, did not call it). For Customer Assistance call 1-800-444-1074
Gulf States Toyota. This was posted on TTORA if I remember right. Was at the bottom of instuctions about the alarm as far as replacing the battery and arm/disarm without sound.
If the number is still active you might be able to get confirmation on what it is doing and how you can possibly change the setting if you are able.
Only other thought I would have, if not the alarm itself, is a wiring or power/ground issue. If just the key was on without the engine running, did you perhaps run the battery a bit low. That could maybe cause an issue as could a battery that is getting weak. Think more that it is probably an alarm control setting, but you never know.
Anyway, hope that helps a bit at least.