Yep, the expansion is a separate download -- if you were looking at the FAQ on the prereleases, that only applied to the prereleases. We just didn't see any need to require all customers to download expansions that they might not be interested in when it came to the official release.
In AI War 3.0, there is an Updates tab that probably has a little (1) on it for you -- you can go in there and download/install the expansion in one easy swoop. Or, if you prefer, you can download it manually from the expansion details page on the left of Arcen site. If you have already entered your main license key for the base game, it won't ask you for it again; if you don't see the place to enter it, that's probably because it remembers your license key from 2.0.
Once the expansion is installed, then on that Expansions tab you can simply click the name of the expansion (it has text next to it telling you to, in that instance), and it will give you a window for the expansion key.
Hope that helps! And, thanks for your support!