CSS Browser Selector automatically includes browser/OS-specific CSS selectors in your HTML.
If everything is enabled and you're still not seeing the browser/OS classnames in your body HTML tag, this is most likely because you are using the Garland or similar theme where it does not output this variable.
The simple solution: modify your
page.tpl.php file so that the tag now outputs this variable, like so:
<html class="<?php print $body_classes; ?>">
The more advanced solution is to write a custom theme function to replace what currently outputs the CSS in your body tag.