spoilers serious question about Halo 4 plot.

So the Librarian imprisoned the Didact in his Cryptum on Requiem
(Halo 4 Terminal).

How was the Librarian talking to the Didact while she was on earth just before the Halo array fired (Halo 3 Terminal) ?

Also wasn’t it the Didact that was meant to fire the Halo Array ?

So is the Didact in Halo 4 meant to be the original Didact not Born ?