Seems I really need to clarify the situation I was in, and how I solved it.
I have an Attack of the B-Team server that I created a while ago. When I made the original post, I had no idea what version the server was running, as it had been several months since I had played. However I knew that the version of Attack of the B-Team that was currently being used on my Technic Launcher was the same version as the server, as I hadn't updated it. Unfortunately, the cog solution was useless to me as my "version" at the time was set to be the recommended build, and as such the cog just showed the currently recommended version of Attack of the B-Team, version 1.0.12. As I knew this wasn't the version I was looking for, I always chose not to update whenever I played, so as to keep the currently installed version, which again was the same as the server.
Now to the solution. I found a file in the bin folder of Attack of the B-Team, not the server folder, just your regular game folders, and this folder was named "version." It wasn't a notepad file, but I guessed that it could be opened using notepad and I was right. Once opened, the file clearly displays the installed version of Attack of the B-Team. It was version 1.0.9c. Since finding that, I have changed my build to "manually select" and set my version to 1.0.9c, as have several of my friends, and we've all played on the server without any version problems, leading me to believe this is indeed the version the server was on as well.