I think I found what the issue was. The addon uses vertex groups to keep track of all of the models you joined together and uses those groups to separate them back out again. I think what I did, was while I was working on arranging my UVs and marking my seams, I had deleted some geometry in the model, which is something that I normally do as I unwrap, because I will occasionally notice stray faces in my UV map. When I did that, I changed the number of vertices my model had which made it so that the addon couldn’t return my model to it’s previously separated state with the texture atlased UVs, so it instead returned it to it’s previous state, which was before I created the texture atlas.
Really frustrating to figure that out the hard way after spending an hour re-arranging UVs, but now that I know that, I know that I have to commit to whatever geometry is in the model when I start atlasing, and delete unwanted faces only after I’ve completed the texture atlas. In the case of unwanted faces, I simply move them off to the side, outside of the 1 to 1 uv space and select them to delete them once I’ve finished the atlas.