Hi from JustAnswer!
The 1993 and up 318si had power windows controlled by the Comfort Module, or the "Body Electronics Control Module" ZKE IV . Before you replace the module be sure that checks are done to insure all inputs to it are not intermittently commanding the windows up and down.
The chances that the BECM is the source of the problem are higher since the windows are acting up even with the ignition off and key out. Sometimes a bad door jamb switch MAY cause the BECM to think you have not exited the car and keep other accessories powered up while you're gone, but it's hard to come up with a combination of two bad components that will cause your exact symptom. 318isi's have had common problems with central control of power windows, locks and sunroof - all of which are monitored and controlled by the comfort module. Relocating the module to the glove box area from the right kick panel solved water intrusion problems but a defective BECM can be caused by simple old age.
ASE Certified Technician
20 years field experience
I again,
The dealer parts man might be able to get further if you called it the Body Electronics Control Module or the Power Window control module. In almost all cases the part number depends on the VIN of your vehicle so supplying him with the Vehicle ID number is all that's normally required. The part number of the module changed several times, and further depends on the factory-installed trim options and you do not want to purchase the wrong module! I know of no aftermarket suppliers for the module remanufactured or new, unfortunately.