I I took a video with Jing and uploaded it to screencast. When it prompted me to view the video, I clicked on the link and could see it there (https://www.screencast.com/t/FnpyAmFp) but when I go into my account it says I have no media files of any kind in my account.
Are you logged in to your account? If you are visiting your library but are not logged in, it's likely the video is in a hidden folder. Hidden folders are not shown unless you are the owner of the content and are logged in. The direct URL to the media still works as you saw here, but we don't allow others to go directly to the hidden folder that it's in.