Hi,
My name is Ahmed and I work for MaxCDN/NetDNA Support.
I'm sorry our documentation wasn't helpful to you as you wish, and I am curious how you couldn't reach our support.
Focing the stylesheet to update is very simple - while we update/refresh the cache every 24 hours, you can force the cache purge/reload of a specific file from the control panel. Login to your MaxCDN account, click on "Manage" next to your zone, and click on the "Cache" tab. You can either purge the entire zone cache or choose to purge a certain file's cache by putting the file path "/wp-content/themes/theme/css/example.css" in the text box and hit "Purge".
I hope that's helpful.
Should you need help, email me directly asamir (at) maxcdn (dot) com.