When you send your transcript through CFNC.org, the information is pulled from the NC Department of Public Instruction's student information system (either PowerSchool or Infinite Campus) and your college should have access to it in just a few minutes. Even so, you'll need to allow at least 2 weeks for the college to process it.
Colleges receive a large number of transcripts and have their own protocols for how the information is added to their student information system. This is why it's likely that if you send your transcript and call the college the same day, the person you speak with will not see your transcript yet in their system.
You can always view the status of your transcript request in the App Hub, (select "View Activity" next to your transcript request), and if you need to call them to ask about the status, be sure to give them your Transaction ID.