I normally also don't do that. But I was recabeling and turned it off minimizing the volume first and when turned it back on I noticed the issue. Then I tried reproducing it without connected headphones
Can you try (powered down and all power/rca/usb cables disconnected):
1) continuity (using multimeter) in the amp: between rca input ground and iec socket ground, and between rca input ground and case
2) continuity in d10: between line out ground and usb ground, and between line out ground and case (for example the screw at back panel)
Also, is amp properly grounded, that is, iec ground pin goes to mains earth via a proper cable?
Also, what device is connected to d10's usb, and how's the grounding in it?