We should be seen a notification of a new message in Mobile

Hi, I am iPHONE user 

- rven if you activate the "temporary" banners or "permanent" banners, I will just be advised of a new message by a vibration/sound, except if your mobile is turned off, in this case I will see a notification of a new message).
But, if my mobile is turned off or on, we should be able to see the notifications when activate "Temporary" banners or "Permanent" banners. I am sure this is normally working. 
Most app what people has using is working like this and don't you think this is reasonable working flow?

Regards
Eric