I'm not familiar with this Chrome extension API, BUT, if someone earns money by letting people install your extension then I'd check that lead.
Eventually, the clients (many IPs you say) that apparently "install" your extension report this event by making an HTTP request - again I only presume!
Saying that, it might be that someone controls many computers which simply initiate these HTTP requests to "report" a (fake) installation, thus making money.
If that is the case, and someone does make money out of your extension (could be also INDIRECTLY) then check the affiliate code or whatever, this is even an issue to report to Google itself, they can certainly investigate that.