Unfortunately it still doesn't work. CSS files come directly from webflow.com export. Maybe I'm messing something up, but there is no too many possibilities to make a mess with. I copy this the line below and change file names. My css files are also in css folder. Don't know what's wrong.
<link rel="stylesheet" href="<?php echo AllInOneMinify::CSS(array('css/file-1.css', 'css/file-2.less', 'css/file-3.css', 'css/file-4.less')); ?>">
Should filename change after emptying the cache? Mine stays the same: css_d41d8cd98f00b204e9800998ecf8427e.css. It's probably stupid question, but I want to be sure - does it assume that the css folder is in templates folder?