You would register them via the Sims 3 site using your Origin login and then they get added to Origin from there is what happened for me. I tried registering my Sims 3 retail copy directly through Origin and it refered me to the Sims 3 site then I bought some of the expansions from Amazon today and added them on the Sims site and the showed up in Origin for me.
It is very confusing how you get free SimPoints so I'm going to explain it here. The base game and
SOME expansions come with free SP to use in their shop. To get these, you have to register your game and then go to the
my page > my account page on the Sims 3 website and there is an orange button that you click to redeem them. I got a link to them when I registered the game but it's a broken link. Their website is kind of jacked up tbh.
On the subject of free SimPoints here are a few expansions that give you free points (or not as noted), we might want to make a list, if anyone got any of the other expansions please quote the list and add to it as I found it hard to find solid information on this:
Sims 3 - YES
Sims 3: Ambitions - NO
Sims 3: World Adventure's - YES
All Stuff Packs - NO
Last but not least, you get free object packs for registering your game when you register on the Sims 3 site. Be sure to note the name of the pack as they are kind of hard to find but you can search for them if you have the name of the pack and download them for free. There is a dialogue that gives you a link when you register but obviously you only see that once.