Sponsors have access to the private repository (I'm using GitHub's collaborator feature). I have several sponsor tiers and $10 a month or more will get you access to my sponsorware, which means you will be added to the private repository and can use the features immediately. What you're effectively getting is early access, so you can use the features before other users.

The official documentation of my project lists exactly which features are "Insiders only", and which aren't. When the features tied to the funding goal that was hit are merged, everybody can use them. I try to always have sponsors-only features on higher tiers to keep sponsoring attractive.

As I understand, Caleb does it with content and entire projects - I'm doing it with new features for an existing project. Also, I'm doing it fully transparent, disclosing how much I earn with this, which I think is crucial to build the necessary trust relationship.