It's not possible to use a private repository as a source for the Docker image used as the build environment for a Jenkins job. After entering the image (ironically created and published to the private repo with the CloudBees Docker Build and Publish plugin), the plugins always downloads the alpine:3.2 image from Dockerhub, instead of the image I've entered from the private repo.

I see no way around this. Unless it's intentional to only support Dockerhub as a source, I think this is a bug.