UPDATE: A hotfix update, v1.1.5.1 was released after this post.
This update fixes a bug where proper credit (and quest progression) was not being awarded after completing the new Colosseum tournament.
Make sure you are playing the latest version- v1.1.5.1 (not 1.1.5). Completing the tournament again should progress the game as normal!
My apologies for the inconvenience