I had it set to "Not In Notification Center" however I still had it set to give me Badge App Icon and Show in Preview and View in Lock Screen.
I thought that if they were in the "Not In Notification Center" it wouldn't show anything however after looking at the settings that's not true. It appears that you have to go thru and tell EACH application what you want and even though it's kind of confusing since it says not in the notification center, it still can show up with these other alerts.
I was just a little confused at to what each section of the notifications did.