So, suppose you have alchemy and you bought the notes on one character.
That character should see the Dornogal quartermaster selling blacksmithing, enchanting, and tailoring as red items, because you are not that profession and you can’t buy those.
A second character who is a tailor and bought the tailoring notes would see alchemy, blacksmithing, and enchanting.
A third character who has none of these and bought none of them would see alchemy, blacksmithing, enchanting, and tailoring.
What they’re showing are the ones you didn’t buy.