I have a 390 with 2x 330a connected via trigger outpur of 390. When I start playback in Roon and system is in standby, it turns on. I can turn it off by using the on-off swtch in the volume ‘box’ (iPad Roon app). As far as I know, it cannot turn of the Moon when streaming stops but if I remember correctly the Moon itself turns of after some time without signal.
Hope this helps you.
Perfect from what I can tell…you might check in roon for the timeout option and or sleep timer to see if it turns off the unit as this works for all my Lumins.