Without having some more information or testing it ourselves we cannot say why.
Firstly, is it just that website that results in two video file downloads or is it any site? If it is just that site are you able to supply us with a link to the website/videos so that we can test it? If it requires login info to view then you can send it to us privately at firstname.lastname@example.org
Secondly, have you tried doing a full reinstall at any point? If there is something broken in Jaksta's processes then a reinstall should reset and fix it.
What you will need to do is delete the app (uninstall) from Applications instead of just reinstalling over it. Then in Finder go to the top menu and then access Go > (holding one of shift/alt/control/command) Library > Application Support > Jaksta Media Recorder and delete that folder (NOTE: doing this will erase your library file list in Jaksta, but your downloaded/converted files will remain intact). This folder and its files may already be deleted when the app is removed, but it's a good idea to double check and be thorough in case it remains and is reused when the app is reinstalled. Reboot the Mac and then do a reinstall of the latest version (https://www.jaksta.com/download/mac/jaksta-media-recorder) and it will regenerate a new copy of the deleted folder and the application files.
Start with that and then we can go from there. If the problem continues then can you also please send through a screenshot.
Im downloading some training videos and it downloads the video twice! Any idea why?