Fixed this issue for myself:
1. Go to thesims3.com
2. Log out (since 99% of people have their login saved.)
3. Log in with your thesims3.com account again (hopefully which has the same email registered as your origin account)
4. Go to your "My Profile" page under "My Account".
Magically all of my expansions showed up.
I had also contacted customer service, which simply told me that the expansions are automatically registered with thesims3.com. No one every suggested "just log off!"
Worked for me, YMMV.
EDIT:
So far, none of the "free" items included with my expansions purchase (I bought Showtime, and Pets) have showed up under "Purchase History" as they are supposed to when you register your game and create an account on thesims3.com. The icons for the game and expansions are all visible now though.
I'm keeping my fingers crossed that tomorrow I'll be able to download my "Freestyle DJ Booth", "Atomic Age Themed Pet Items", and "Paws and Whiskers Costumes Set".
The seperate "Origin-al Beats" Stereo included as a bundle with Showtime worked flawlessly, but had the www.thesims3.com/incentive/ShowtimeOrigin incentive URL, and was still up. The one for the costumes for Pets, unfortunately has been automated away with a message simply saying that the incentive will show up in your "Purchase History".
Double Edit:
Just noticed that whatever incentive there was to register Generations, also likely isn't there. (I'm not sure, as the purchase confirmation email doesn't actually tell you what it is you're supposed to get).
Looks like I'll be making another call / chat to customer *sigh*
