There are two ways to prevent incoming performances from playing automatically: sleep mode and do-not-disturb mode.
You can put your Oda system in sleep mode by holding the top button down for three seconds. While asleep, the system will not automatically play incoming performances. You can wake the system back up by clicking the top button once (it may take a few seconds to fully wake).
You can also create a do-not-disturb schedule in the app. You'll have to be logged in to your Oda account to do so. If you are logged in, "Do-not-disturb" will show up in the settings menu. Incoming performances will not be played automatically during the times you designate in your do-not-disturb schedule.