edimax

Thanks, I’ve managed to work this out with support from my hosting provider. Suggestion that worked was to point out each domain into separate, default /public_html/ folder with WP installation (instead of my current setup where every domain points towards one /public_html/ folder with WP). So the folder structure on my account will look like this:
..
/domains/phrasecityA/public_html/<WP installation>
/domains/phrasecityB/public_html/<WP installation>
etc

Support also said that the folder structure I’ve described shouldn’t cause problems, but to be sure they advise to not use it when there is another, better solution.

Guess I can mark this as resolved.