how the capacitor works.
the capacitor is like a huge battery with a short memory span. when you turn your stereo on, it charges up to full voltage; power fills the capacitor every time you start your car. when you turn off your car, it still holds the charge, and will continue to do so until it is drained. this means you will have it appear as if it is still on after you shut the car off. it isn't retrieving any more power from your battery; rather, it is slowly going to drain as it cannot sustain a charge for a long period of time.
it is normal operation for it to display "on" long after the car has been shut off. it will not drain your battery this way. again, this is just how capacitors work.