if you see the data in MP3tag, then everything should be fine - so perhaps Groove Music has a problem.
If you want to investigate yourself:
Check the files' integrity (e.g. with foobar, mp3diags and/or mp3val - all currently freeware)
Check, which tags you have in the files: perhaps you have different tag versions which are out of sync. Esp. the combination of ID3 tags and APE often causes chaos.
If you have APE tags: remove them.