An easy solution to transfer your Smart Playlists from iTunes or Apple Music to another service, is to copy the content of this Smart Playlist to a normal playlist.
For that, simply go to your Smart Playlist iTunes / Apple Music, select all songs (you could use ctrl-a) and then click File => New => Playlist from Selection.
That's all ! Your songs are now in a standard Apple Music playlist and could be read / displayed on Soundiiz directly.