Keep the Hushed app from appearing on your main screen every time a message or call comes up by clicking the gear in the top right-hand corner. You can then choose to toggle off/on "In-app sound," "In-app vibrate."
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.