As a store owner you will be able to restrict access to who may or may not use the StagingPro app though through your BigCommerce user permissions however, once you give Administrator rights to the agency they will be able to send changes to production.
Administrator permissions are assigned to GitHub so, if you have advanced knowledge of GitHub you could retain admin rights yourself while giving contributor or viewer rights to your agency. Please contact your agency first though because this may cause difficulty to your project,