If you are using MC on two different computers, with the same files, and NOT using the Client/Server features of MC, I think I know what's going on.
In this case, you are relying on the files as the repository for all metadata changes you make (album, artist, etc). MC has it's own database for metadata that's stored outside of the files. There's a setting that tells MC to write as many metadata tags as it can to your files. Files only support certain tags, so you should get most everything, but anything non-standard (like Composer for example) might not get transferred to the files.
The setting to make MC write tags to files is: Tools > Options > General > Importing & Tagging > Update Tags when file info changes
Do this on the computer that you are using to make changes. If you make changes from both, it gets trickier.
You will probably want to manually tell MC to write all tags to get everything started. Go to Tools > Library Tools > Update Tags (From Library) . That will write the internal library (database) to the files.
At the other computer, where you want to read the changes that were made to the files, you might want to manually sync that too: Tools > Library Tools > Update Library (from tags). To make the updates happen automatically in the future, you'll need to tell auto import to look for changes: Tools > Options > Library & Folders > configure auto import > Tasks > Update For External Changes
Good luck to you.
Brian.