On my iPhone 6, running iOS 8.2, I get a second new text notification 2 minutes after a text arrives.
For example, here is the sequence of events.
Phone is locked.
Text arrives, and I hear the "Ding" and text message details. It says something about New Text message, now.
The phone auto locks and goes back to sleep.
I do nothing.
Then, I will hear, New Text 2 minutes ago, in a second notification 2 minutes later.
This is consistent. Is it also normal?