When a contact that has never talked to you before send a private message, that very first message will fire a notification on your registered devices (iphone, android, ipad, tablet, etc). Devices are registered on every login and deregistered on logout.
Once you estabilish contact with someone, your registered devices should receive all notifications from that person in background (app closed or minimized) and increase the app badge counter. Badge counter is reseted once you open the app.
When a chat group is visited you automatically opt-in to receive notifications from all the users inside that group.
You can always decide later on from whom you want to receive push notifications, both for groups and users.
You can also silent an user or group directly from the chat using the menu option (three dots) in the top/right corner.