Figured it out! 2 bugs (features, rather?) combined:
The tab you are on is persisted. So if you ever go to "all" tab, all subsequent chat visits will go there as well.
The "all" tabs STILL shows Politics.SE as a site as part of URL, which may be technically needed for other tabs to work but confused the heck out of me, since it looked like I was looking at the site specific tab.