Turn them on from the More screen, under Notify this device.
You get notified when a customer replies, when you are mentioned, or when work is handed to you. Nothing else. A product that notifies you about everything gets its notifications switched off within a week.
If they are not arriving
Check the status page first. Apple push requires a key configured at the platform level, and the status page reports honestly whether it is set up.
After that, check the phone's own notification settings for the app, which people commonly decline on first launch and then forget.