Cross post here, I must have been typing when Michael posted.
I found some instructions on Victron B to B chargers and I think I may understand the 12.5v setting now. Interesting to be sure and may apply to many of the newer, but not older, vehicles we all have.
Here is a partial quote from the instructions explaining their "engine shutdown detection" feature.
It is from this document in section 5.
https://www.victronenergy.com/media..._-_Isolated/en/engine-shuthown-detection.html
Engine detection to confirm actual running is a great feature, but newer energy conserving alternator controls look to be giving their setup some issues because of low voltage.
This confirms they do not want the B to B connected when the engine is not running, I think, but when set at 12.5v it easily can be with the engine off depending on the battery condition. It almost certainly will stay connected at initial shutoff of the engine until the starting battery loses it's surface charge.
I don't know what a good solution would be if you have a van controlled alternator that drops that low on regeneration or such because if you turn up the setting to the more normal 13.1v detection you will have the B to B turning on and off a lot during normal driving. If you set it lower like the OP has it will stay connected when not running, which you don't want either, if the engine dies. It probably will disconnect if the key is off, or it should, because the power to the B to B should be coming from a switched, not continuous 12v source off the ignition switch. If it is a push button I don't know where you would find that source, but probably a PCM controlled relay.
If you have an older van, I would just turn up the setting to 13.1v so the B to B can't be on with the engine off.
The better way to sense engine running is to use a "stator/tach" output from the alternator that will show if the engine and alternator are actually turning.