Songbook not defaulting to book instrument...

I recently bought a ukulele and am attempting to set up a second song book for it...
My Process for an unexpected page behavior...
I've created the second book 'Uke' and set the default instrument to Ukulele C-Tuning.
I return to 'My Songbook' and copy a song to the 'Uke' book.
I then view 'Uke' book and select the song. 
It's still says Guitar and I change that to Ukulele C-tuning and transpose it a few steps.
Return to the book and back to the song and the page keeps the transpose but not the instrument selection... 

Is this the expected behavior?   Do I always have to select the instrument tuning?

Edit:  I just noticed that the copy of the song in 'My Songbook' has the transpose I set in the 'Uke' book.  I guess I can not have the same song saved with different transpose and instrument tunings in different books?

Thanks
Keith