I ran into a SaaS company recently that had a guide for how to setup a white-label domain using route 53 and Cloudfront for one of their services. The SaaS company charges for service bandwidth usage, and they host their infrastructure on AWS, so if you opt to follow their guide they get a fat margin bump in the form of avoiding an egress charge and you get to be double-charged for bandwidth. You've gotta love it.
If I follow what you're saying I suppose my understanding could be wrong, but there's no "cloud transfer" required. It's just a matter of both the distribution and the configured origin being on AWS. If the origin doesn't direct traffic outside of the datacenter, AWS doesn't bill that as egress to whoever owns the origin. The Cloudfront distribution, on the other hand, will take the hit once it exceeds the free tier because it's the AWS service distributing data to end-users. It has to make a request to the AWS internal service then cache it, so The SaaS lambda or s3 bucket or EC2 instance or whatever they're using is none-the-wiser. It's just how the AWS billing mechanism works.
AWS has notoriously high egress fees.