By it still has service you mean...It still has the ability to make/receive calls and use data or it displays that it has cellular signal?
iPhone 4's have a different SIM than the iPhone 5's do so I would assume that the Genius bar didn't bother taking out the sm from the old phone. If this is the case, your phone will still pick up a cellular signal when on. However, it should not be able to use the cellular data or make any calls except for emergency calls which is required by federal law.
If you are able to use the old phone as you normaly wouldl then you'll need to contact your carrier and make sure they unassociate the old device with your account.