They might be referring to the Armstrong type starship USS. Excelsior NCC-1729? Which was mention in the book, but not in the movie itself. Also there suppose to be a model of the ship itself. It was one the ships that Nero destroyed.
The "Armstrong type" ship was the U.S.S Armstrong. There was no ship labeled the Excelsior in the movie.
Weller is not Captain Styles; he's Commodore Decker of the Constellation.
Cumberbatch is Trelane, pulling a Q and masquerading as a human but unlike Q, doing it covertly to study humanity.
I'd ask you for a source, but I'm guessing you just made that all up.