By default notifications on iOS are suppressed when full device mode is enabled. This means an agent can not see any notification that might come through during a live cobrowsing session.
This setting can be changed from within Settings > Notifications > Screen Sharing but this is off by default.
During full device mode on Android all notifications are visible to the agent. However if the user enables Do Not Disturb mode then notifications will not be shown to the agent.
We recommend adding this to your agent's script to first enable Do Not Disturb mode before continuing with the full device cobrowsing.
If you wish you can add support to your own application to automatically turn on Do Not Disturb mode when a session goes into full device mode but this will require additional permissions for your app.