From More > [your name]'s notifications, you can choose which kinds of updates actually reach you — new events, task reminders, new sheet music, and so on.
This setting is per band, not per device. If you use multiple accounts on one device, each one has its own independent notification settings — muting reminders for one band never silences another.
These settings control what Mozzy sends you as a push notification (and logs in your in-app notification list, see Viewing your notifications) — they don't affect what your band's admins can see about you.