Thank you for the information! This has led me to do some more testing.
So indeed it is caused by current coming into the RCA outputs, not the USB (my bad! I'll edit my previous post to reflect this).
I tried 3 cases with video:
Case 1: I turn off the receiver (off-screen) with the D10 output connected to the receiver. It clicks.
https://streamable.com/yj6hr
Case 2: I turn off the receiver (off-screen) with the D10 output connected to a turned off O2. It clicks. Notice how I don't even touch the O2.
https://streamable.com/18hc1
Case 3: I turn off the receiver (off-screen) with the D10 output not connected. Nothing happens.
https://streamable.com/xi92f
Case 1 is most possibly caused by current coming from the receiver, but Case 2 is funky because I guess the current from the receiver is getting into the O2 and coming into the D10 output, making the relay click.
I don't know if it could damage the D10 (it doesn't lock up, it's just the relay and screen that lights up) but for now I'm disconnecting the RCA before turning off anything just in case.