I'm sorry. Let me explain.
The next time you log into the game, you have a box next to your character that is to be race changed. You click the box, make the changes, and enter Azeroth.
When i race changed, I was in game on one monitor, and paying for the race change on the other monitor in my account manager. Because I was already in game, i had to exit game and re log in to see the changes.
The changes were instant as soon as they billed my credit card.