key off ignition should shut off due to no power as well as ecm and fuel pump
only way i see it could stay running with key off is the oil sender switch 12v power wire is not connected to a switched source and is back powering the car (ecm , pump and ignition) as long as oil pressure is above 4psi which would take a few seconds after key off
do you have anything plugged into the fuel prime wire behind alternator