I was curious as to who was making the money via the sponsored ads that are displayed on the first tab and the web tab of this plugin.

As it turns out, the sponsored ads are for Google because the Ajax powered API is so new. Here is the 411 on the issue.

That is a really great question that I had to search awhile to find. The answer is because this Search API is still so cutting-edge new, Google is the only one making any money from these Ads. It is still pretty beta now, but in the future it will very likely have the features we want. It is against the TOS to remove the ads, and currently you cannot hook your own AdSense account into the Search API. You can however use css to re-position the sponsored links.. like:

.gsc-control .gsc-ad-box {padding-top:100px;}

Does the AJAX Search API contain advertising?

Yes. The Web Search results may include up to 2-4 clearly marked sponsored links. There are currently no ads displayed among the News, Video, Maps, or Blog Search results. If you’re interested in earning money for displaying relevant Google ads on your site, you can do so with Google AdSense.

Thanks to AskApache for clearing this up.