Look at the name of the CSS resource that was "render blocking above the fold content".
If that resource is native to your site, then what happened is the CDN loaded the cached CSS in the initial part of the page that was originally not render blocking above the fold content. There is nothing really useful that you can do in this regard. If there is a specific URL for your mobile sites, you can add a page rule and prevent caching of content for mobile pages. Use tools such as Pingdom Speedtest and check if there is any considerable increase in speed on using the CDN. If not, I would recommend disabling it.
If the CSS file is not a resource of your server(highly unlikely), then purge the cache and try again.
