Interesting. Does it actually start?
I'd pull the key fob(s) apart replace all the batteries on them and make sure the start button is not compromised. Dirt and debris can make the button touchy
. I would think that is a strong possibility but would think the engine would start and run for 10 or 15 minutes.
You might also check the engine battery voltage. Many SMB's especially the older models using the surepower separator are configured to use the house battery to assist start the vehicle. If the starting battery system is low, I've found the engine sometimes tries to start itself because the alarm is corrupted due to low voltage but once the command is given to start, the separator supplies enough voltage to start. Whether the engine starts would vary. If there is no supplementary starting system or SMB designed so you manually have to jump start the vehicle I'd be looking at somebody checking the alarms electronic computer and connections.
Lastly most alarms I've been told are supposed to scramble the code each time they're used. I'm not too sure about that. Maybe a neighbor's alarm is throwing a similar start command? I would think if that was the case the van would start.
Last time I had that happen on my work truck it was something resting just right on the extra fob I don't regularly use
Took me a while to find the fob