I have noticed that when some users do a search using duckduckgo. Instead of sending the users directly to the content website duckduckgo uses a redirect method. While redirecting duckduckgo can possibly monitor/log what urls a user clicked and other details also. Google search currently uses the same method to monitor user clicks.
If you want to check whether your searches are being redirected in duckduckgo then do these steps. First do a simple search in duckduckgo. Then select a random result and copy the html link. Paste the copied html link in a notepad and see whether the link starts with duckduckgo.com domain.