I ran into this exact issue. There are three major brands of GM interface harnesses. Metra Scoshe, and CRUX. I purchased a scosche from walmart and has this exact problem. You NEED the Metra interface, which crutchfield offers. I purchased my setup from them along with the Metra GMOS-04 and it has worked beautifully.
The databus in these cars is in the radio, the interface acts as an emulator would. I talked to someone at a local car audio shop, he told me that in many cases, the cheap interfaces can shutdown the PCM (kill your gauges, along with other uglier problems, it can even overheat your engine by knocking the temperature sensor offline and failing to start the engine fans), and in some cases, mostly on GM trucks, it can FRY the pcm.
You should return the CRUX interface, (i know it was cheaper) and get the Metra. The chimes are still faint (only when the engine is on for some reason), but it does what its supposed to and keeps the computer happy.
Good Luck!