Cloned Sites and Original Site Are All Affecting Each Other
I just figured it out. I have a wildcard SSL setup for my server. By default when you clone a site in Aegir it does not set it up as SSL. However, I was still able to access the cloned site via HTTPS.

The issue was caused by accessing the site via HTTPS when SSL was not enabled in Aegir for that specific site.

As soon as I enabled SSL for the site in Aegir the problem went away. 

I'm not exactly sure what was going on in the backend. It would be great if someone could chime in on that...