GEN 2 12v cigarette and AC inverter powered on if truck is off?

Does anyone know if the 12v and AC inverter will shutoff at somepoint after I've turned off and locked my truck? I've got some stuff plugged in there, but even after I lock my truck, I can still see the little lights on my devices stay lit for several minutes.

Anyone else have thoughts on this? I don't want to leavesomething plugged in a drain my battery. Thanks!

There is a delay on the 12v and I think the inverter is on/off with the truck engine.