Right, sometimes it's quite problematic to use this extension. If you have dashboard.site.com opened in a different container, you have to left-click the extension icon and select "Always open this site in...", then choose the same container as for login.site.com.

Then you have to start over.

Thanks - that technique worked on another site, but the site in question never gives one the opportunity to "always open site" because it automatically switches (in this case) dashboard.site.com back to login.site.com. Theoretically, it should be possible to track through all the additional URLs the site is going to open (before assigning any to the target container), then, starting from the end of the chain, put each URL in the target container until you get back to login.site.com. I haven't actually tried this yet, as the site opens a lot of URLs.

I have verified that one can get the entire set of URLs into the container by starting at the last URLS in the chain and adding them backwards, finally ending with the login URL. A bit tedious, and prone to redoing when one either discovers another previously unknown URL, or the site adds or changes to the current set.