Yes, welcome to Saxfiend. Nice name.

Audiotrack, maybe I'm missing something but I think the question is this:

Create a song in the key of D. The most important step is to set the key signature to D (not leave it as C, the default).
Add chords of B and F#
Use the key signature pull-down, left-hand column, to change D to E
The chords now are showing as C# and G#

However, this transposed the audio up a step.

If you want the audio to remain in concert D, then the better way is:

Options, Preferences, Notation, Transpose, change 0 to 2.
Now the chords are still showing for tenor sax C# and G#, and there is a little "+2" in the key signature, giving you a visual indication you have a transposition in effect visually only. The song still plays in Concert D so you can play along on your tenor sax. Since you said "transposed display for tenor" I think this is the way you did it.

So, to Saxfiend, it works correctly for me. Therefore, it would help to know if you are on a Mac or Windows version (Windows here), and what year and build of BIAB you are using (2022, Build 920 here). Find this in Help, About. That might make a difference in what you are getting. Then tell us exactly the steps you are using to transpose (as there are several ways to do it).

BIAB 2025 Win Audiophile. Software: Studio One 7 Pro, Swam horns, Acoustica-7, Notion 6, Song Master Pro, Win 11 Home. Hardware: Intel i9, 32 Gb; Presonus 192 & Faderport 8, Royer 121, Slate VSX, Adam Sub8 & Neumann 120 monitors.