All I needed to do to make playlists appear was to create proper M3U files and make the server software refresh its index.

Do you have proper M3U files for the playlists?

(M3Us are ASCII text files with the extension of .M3U that contain, one on each line, the path and file name of the MP3 file. You can use programs such as WinAmp to create M3U playlists, or you can make them yourself in a text editor program).