I've done some customisations to the theme in customise.css like you said.. but nothing's changed. What gives?

One version of the theme included a secondary customize file which is no longer in use.

This is why you don't see the changes.  It's a VERY quick fix.  Just move the changes you added to customise.css.liquid, to customise.scss.liquid.

They'll show up then. This has been fixed in recent versions, so should affect only a very small number of shops.

Done!