It is hard to know exactly how any given site detected that a downloading program was being used. Different sites may use different methods, we would have to test it to judge what it is doing. Are you able to say what site did this to you?
Prior to version 1.4, Jaksta detected video streams and opened an "extra" stream to download them. You could override this behaviour in the Downloads tab of the Preferences by choosing "Always Record HTTP/RTMP". This makes Jaksta less visible but means you have to leave the video running in the browser.
From version 1.4 onwards, Jaksta uses a local proxy daemon to capture video, redirecting all browser traffic through this proxy. This change was necessary to capture video over HTTPS.
How does a site serving videos detect that one is using Jaksta? What is the particular "Jaksta" signature or behavior being monitored? I know this because access was working -- then not -- complete with a nasty automated reply. Does Jaksta initiate two download streams? Does it pull down info just too suspiciously fast?