MusixMatch is actually another company entirely that allows Spotify to use Lyrics. Any lyric issues would need to be addressed with their support team. They can be reached via their commuinty at https://www.musixmatch.com/community
Actually this does NOT seem to be a Musixmatch issue but an issue with the Musixmatch integration in Spotify.
I also thought my lyrics weren't saved but found that they were actually updated directly on Musixmatch website but in Spotify the old lyrics were shown for days (if not weeks). It therefore seems to be some nasty caching issue.