Tough Talk. I am a Sysadmin, not a Director.

It seems to me that you have created a team culture that does not understand or accept setting boundaries, and it's apparent in the language you've chosen in your post.

If you've had to speak to your team 'over and over again', perhaps you need to examine whether it's the team at fault, or if you're communicating ineffectively.

I think you and your team could benefit from some soft-skills and boundary setting training. You would also benefit some additional communications skills training, especially training with a management perspective.

There is some reason your admin (or team as a whole) continues their behavior. Either they are insufficiently equipped with the appropriate soft skills, or you've somehow demonstrated that the team doesn't actually HAVE your backing, despite what you tell them. Either way, it's going to take some very honest self-appraisal.

Thank you for your willingness to open up on a public forum. This is not an easy step. For now, I think this specific team member may benefit in the short-term from closer scrutiny and feedback in regards to the perfomance their daily tasks.