Based on my understanding of the question, the operator creates deployment objects for other components. However, in this case only the deployment configuration is created by the operator. It is the Kubernetes Control Plane that actually pulls the image instead of the operator pod.
If the image is present in a public repository, then there should not be any problem with pulling the image specified in the deployment configuration. If the image resides in a private repository, authentication details for the registry must be provided to the Kubernetes control plane. The operator must create a secret containing the authentication details of the repository and provide them in the deployment configuration. The doc explains how to do this using Kubectl, but your operator can do the same thing.
Link: https://kubernetes.io/docs/tasks/configure-pod-container/pull-image-private-registry/