I had the exact same issue. Are you powering your speakers directly from the headunit or through an amp? I'm waiting for my amp, so I tested my install with the stock amp...and it wouldn't work.
I had the power antenna wire from the deck going to the power antenna wire on the GM harness and it didn't work, so I wired the remote lead from the deck to my factory harness's power antenna wire and it fixed it. That's why it works with the radio on, because the deck's power antenna wire sends out a signal when the source is the tuner, but not when you switch to USB mode.