Not completely sure what you are referring to re: Google as there is no connection at all between them and DDG.

WIth Firefox (or any other browser), your browsing history is maintained locally unless you take steps to disable it. You can take steps to disable or delete this local storage of your search history but it is not something that DDG or other web sites have any control over. Browser history is fully controlled by the browser and should not be confused with tracking, in which your search data would be stored and shared with others (which DDG does not do).
These pages will help:
posted by x.15a2 Community Leader3 years and 11 months ago Link