Sure sounds like it is wired wrong. From the radio there should be up to 4 wires, Ground, ( usually black) Always on(usually red), On with ignition( usually orange I think), and lights(usually yellow I think). The always on wire should use very little current as it's function is to keep the station presets. The on with ignition actually powers the radio and turns it on. The lights is solely to turn the radio lights on / off with the vehicle lights, many radios do not have this anymore.
Get a test light and verify how it is wired. Not sure about the yellow / orange wire colors