Don't know if it's an error, but it is the other way around (Alexandria can't build war fleets from the start, Antiocheia can).
I think someone said one shouldn't really take to heart what the building browser says, but Alexandria starts with a small port (so it can only build raid fleets at the start of the game), but can build royal fleets from the "port" building, while Antiocheia and Akko can only build royal fleets from large ports. Is this intended? Also, was the Phoinike region supposed to build Royal Fleets?
Couldn't really explain my point. This is a bit nitpicking, but from the detailed explanation you gave, I wondered if Carthage port would have a similar production output to Alexandria and Antiocheia (and Akko?). If they did, a +1 in their unit pool could be added to Carthage "large port" building, comparing it to the other large ports of the time. Not that it matters really in the great scheme of things, since western northern Africa has allot of places to build war fleets. Like I said, nitpicking