When I was first trying to configure W3TC, I noticed that if that checkbox was unchecked, then W3TC would generate the files in the following directory, because it used minify.php directly in the url.
/wp-content/cache/minify/000000
When the box was checked, the files were removed and then they are generated when the file isn't there by doing a rewrite that points to the minify.php file.
Craig