That's something normal to happen, especially on browsers other than Chrome. To solve this issue, instead of left clicking the Download Video link, Right Click -> Save as... and choose the location you'd like to save the video to.
Currently FB Downloader works just fine with Android using Chrome browser. As for iOS you should use a file manager, we suggest using FB Downloader with this app Turbo File Manager in order to save videos to your camera roll and view them offline.
Videos that contain Copyrighted Music are the most affected. We've found a solution to this, just Click "Video with No Audio" on the download page of your video and you'll be able to convert the video with audio.
FB Downloader doesn't store videos neither we keep copies of downloaded videos. All videos are hosted on Facebook's servers. Also, we don't keep track of download histories of our users, thus making using FB Downloader totally Anonymous.