To keep your Hushed app from appearing on your main screen every time a message or call comes up by turning these off by clicking the gear in the top right hand corner. Then you can choose to toggle on In-App Sound , In-App Vibrate , Hushed Events
Using an Apple device you can also change notification display options.
1) Open the Settings app
2) Click on notifications
3) Click on Hushed
4) Copy the settings from the below screenshot
Make sure "Allow Notifications" is enabled as this will allow the app to function in the background.