Playlists made in the Apple TV app, work through Home Sharing for local media that is compatible with Home Sharing. So: not for iTunes Store purchases online, not for iTunes Store purchase downloads in HLS format (.movpkg). Instead: .mov/.mp4/.m4v files with H.264 video. Empty playlists, or playlists with all incompatible media, or playlists with media of a different category may not show under Movies in the Computers app.
Playlists are intended to play multiple videos consecutively. It is not an organizing tool, and using it that way may be disappointing on multiple levels.
Media that is not tagged as ‘Movie’ or ‘TV show’ (or not tagged at all) would be categorized as Home Video in the Computers app.
The Computers app should notice new additions of media quite fast, without manually reloading anything; the same goes for new or altered playlists.