I'm not so expert with Donotdisturb.
Here is the info from the manual.
Do Not Disturb and Notifications
Push notifications appear in Notification Center and alert you to new information, even when the associated app isn’t running. Notifications vary by app, but may include text or sound alerts, and a numbered badge on the app icon on the Home screen.
Turn off all notifications: Go to Settings and turn on Do Not Disturb. When it’s turned on and iPhone is locked, all notifications and calls are silenced, but alarms will still sound. You can set the following options in Settings > Notifications > Do Not Disturb:
Automatically turn on Do Not Disturb: Set the starting and ending hours for when you don’t want to be disturbed. iPhone turns on Do Not Disturb during these hours each day.
Allow some phone calls during Do Not Disturb: When Do Not Disturb is on, calls are silently sent to voice mail. To allow some callers to ring through, tap Allow Calls From. You can allow calls from your Favorites list or other Contacts groups you define. For information about Favorites, see Chapter 25, Contacts, on page 100.
Allow persistant callers to ring through: Turn on Repeated Calls. If the same caller (based on their Caller ID) calls you twice within three minutes, iPhone will ring.
Turn an app’s notifications on or off: Go to Settings > Notifications. Tap an item in the list, then turn notifications on or off for that item. Apps that have notifications turned off appear in the Not In Notification Center list.