iMessages don't appear until I unlock my phone.

Every other notification I get on my iphone, I still get when the phone is on the lock screen. Some notifications I have set so that the actual text of the notification doesn't appear on the lock screen, but the phone will still vibrate or make an alert sound when the notification is received. However, it seems when someone sends me an iMessage text message, I will not receive any alert at all until I unlock the phone. Then, suddenly the phone will vibrate with all of the text messages I received, and if I haven't checked my phone in a while some of them could be from hours ago. Why aren't I getting alerts of new messages immediately when the are sent? I'm pretty sure all of my setting are correct but maybe there is something I'm missing.