leokennis The extension will attempt to redirect any searches to the search engine urls that it has permissions for. If you either granted permissions across all websites or granted permissions individually to multiple search engines, the redirects would happen when you use your search shortcut to switch to any Safari-supported engine. The extension popup can tell you which urls it has permission for (click the Extension icon in Safari's location bar, then tap Kagi for Safari icon).
Ultimately, you'll need to go to Settings App -> Safari -> Extensions -> Kagi for Safari
and remove permissions for the search engines you want to prevent redirecting back to Kagi. "Other Websites" should be "Ask" (in English locales… not sure about NL locale).