Settings >> go to Notification Center >> You Tube >> Then you can set it up with how you want it banners, alerts, show in notif center, lock screen...
(make sure you have YT in "include" section of notifs)
btw, I notice sometimes the notifs don't come through. I have mine set up as "alerts" and a few will come up, others not...idk why...odd. Maybe a bug? hmm..