I had this same problem.
It occurs in some missions that were made before Base 3.3, as far as I reckon.
I think the table entry for Babylon 5 was changed between Base releases 3.2 and 3.3... so most missions and campaigns that were made before 3.3 use different entry to call B5 into the game, and when Freespace doesn't find the correct ship from the table, it always puts the first ship in the table into the game instead of the correct ship.
In basic Freespace and Freespace 2, this "first fighter" used to be GTF Ulysses, in TBP it is the StarFury.
Solution for this problem - wait for new mission releases that patch this problem.
Or if you can FRED, change the entries for Babylon 5 in missions to match the current entry in the ships table.

Someone correct me if I got something wrong.