Panel on different (sub)domain — cache?

One of my clients has an installation with the panel running on cms.example.com while the live website runs on www.example.com.
Now I realized the cache does not get cleared when they make changes in the panel. Is there something I can do about it? Thanks in advance!

Hm, no idea atm. Have you tried to set the URL in config.php?

Setting the url in the config does not work because the panel is only accessible via cms.example.com, not via www.example.com. The url seems to affect the panel too.