The DuckDuckGo extension is to provide duckduckgo searches using chrome, DDG's ads on 'their' site doesn't track you while your browsing the search results or when you click, however once you reach the page of the link you click on, then and only then are you probably catalogued and or recorded. But thats the independent site you visited not DDG. DDG can't force the websites you visit that you found using their service to not record or track you once you get there. In otherwords, ads can and do track, but the ads displayed on DDG do not...

"We do not use any third parties to do the code insertion, and we do not work with any sites that share personally identifiable information (e.g. name, address, etc.) via their affiliate programs. This means that no information is shared from DuckDuckGo to the sites, and the only information that is collected from this process is product information, which is not tied to any particular user and which we do not save or store on our end. It is completely analogous to the search result case from the previous paragraph--we can see anonymous product info such that we cannot tie them to any particular person (or even tie multiple purchases together). This whole affiliate process is an attempt to keep advertising to a minimal level on DuckDuckGo."