From what you describe, it seems like either the USB part of the Dac has problem or the driver of Synology NAS has bug. You can try:
1. Use notebook or PC to play the same song with DAC, if no problem, it proves the USB part of the DAC is ok
2. "borrow" a "usb to coaxial" box to try NAS -> usb2coaxial -> dac, if ok, then buy one. Otherwise, it is driver of NAS that has problem.