Yep, that is what I thought. You need to use the "Update tags (from Library)", not that other way around.
What I'm not sure of these days is if the [Rating] tag is written to the file by default. It is with my Library, but I may have changed that setting at some time from the default.
Go to "Options > Library & Folders > Manage Library Fields > select the [Rating] field and check that the "Save in file tags (when possible)" setting is checked. It may be unchecked by default.
Ratings set and saved this way are visible in Windows Explorer, as well as other tools. It is common not to save this tag to files, as it is a very personal thing, and is often left in the Library only.
The terminology I use is:
Field = metadata stored in the MC Library.
Tag = metadata stored in file.
That works for me, and I try to use that terminology consistently.