I realized that importing cue files into MC doesn't automatically split the files into separate tracks. I searched the JRiverWiki and found that splitting can be done within MC, following
https://wiki.jriver.com/index.php/Cue_Files and the cited link to Listener's explanation of how to split cue files. Well, I followed the steps: after importing, I used the commands 'Rename, Move & Copy' > 'Copy and update database to point to new location'. First, I attemped this with one album, and it worked out just fine: the separate tracks were copied to the directory, there were no unexpected changes to the tags or whatsoever. Then I decided to do all the albums which needed to be copied, and did a bulk copy process. First I thought the overall size of all files was a bit too large. Well, I was right in sensing something weird. The files that had to be copied into the directory, did copy with corresponding filenames, but the tracks all contained the entire albums (I didn't check that when testing), and in the library, all the tracks were replaced accordingly, that is with flac files containing the entire albums.
I'm curious whether I made some stupid error myself (or rather that the post referred to in the wiki is faulty), or that this copy functionality itself is defunct. What is the right way to split and copy cue files into separate tracks (with corresponding files)? Is that even possible within MC?
Hope someone has some suggestions.