parsing of the css happens regardless of cache, ie it must parse it before it can cache it on the server so I don't understand how cache could be the problem.
The only issue I know of with csshandler is that is you use background images with url() the image file name must have single quotes ie url('myimage.png') not url("myimage.png") and not url(myimage.png)
otherwise it cannot resolve the base path for the image correctly.
When I view your site in Chrome it looks fine to me at the moment.