Thanks for your response. I did work out the issue but forgot to post back here.
Although I had deployed the package to the server, and I was right clicking on the package on the server, I was doing it from a local instance of SSMS connected to the server. Apparently when you run a package that uses an environment variable, the environment variable is read from the system where the package is being called from. In other words since my SSMS was on my laptop, it was reading the environment variable from my laptop. When I logged onto the server, and opened an instance of SSMS there and ran the package it worked as expected.