Documentation will be updated after Scripts Organizer version 3 is released.
We lied on this one a little. It's actually two clicks since we introduced the confirmation dialog box.
When changes are approved by your client or you are happy with the result to back to Sandbox Settings and hit Publish button.
Once the button is pressed you will get a confirmation dialog box.
Once publish is confirmed you will be redirected to Oxygens Settings, CSS Cache tab, and regenerate CSS will be triggered automatically.