Just an FYI, I don't have apache installed at all.
When I disable the fancy links, it does work. However, this is not acceptable due to the query string which my cdn does not like to cache.
Again, I'm using the rewrite rules that w3 generated for me. It places them in the nginx.conf which is the equivalent to the .htaccess file.
rewrite ^/wp-content/cache/minify/(.+/[X]+\.css)$ /wp-content/plugins/w3-total-cache/pub/minify.php?test_file=$1 last;
rewrite ^/wp-content/cache/minify/(.+\.(css|js))$ /wp-content/plugins/w3-total-cache/pub/minify.php?file=$1 last;