Notifications
On a phone with the Halvies app, a push comes straight away when someone settles up with you, puts up a bill for you to pick from, or says an expense isn't right (and when they answer yours). Each expense that includes you can come by push too, if you turn Expenses on.
A settle-up is emailed straight away to the other people in it. The daily summary at 07:00 lists what other people changed in your groups the day before, and only comes when something did. You're never told about your own changes.
Turn any of them off under Notifications in the account menu. Each email also has a link at the bottom to stop that kind.