Engine Off, Keys out, CD still playing

[Lithium2]

My E39 still have the original BMW ICE, I have a problem here. If I switch off the player before I switch off my engine, the player or radio will still continue playing.....I assume this is wiring problem? The ICE is wired directly to the car battery? I plan to send my car to brother peter's to check since they install a lot of ICE for BMW and Merc.... Or is there any other good accessory shop to recommend? Thanks.