I don't remember in great detail (the app still exists, probably works, I/we could poke at it if so), but I think it was an always thing. By making a bookmark you included the session data, so by logging in and making one you ensured you were always logged in after clicking the bookmark.
Yep, still works. And reminds me why I liked it - small and fast :| Chrome has gotten so slow. Firefox is no better.
So, I'd probably recommend trying it yourself too (really, it's a nice alternative browser. many are horrible, this one I used happily for quite a while), but you can only really trigger the behavior by starting a "single-session tab" which is cmd-shift-T instead of cmd-T. Single-session tabs are basically the same as a "private" window, but if you save a bookmark, you save the session.
This is all reinforced by having the bookmarks bar (on the left) primarily populated by dragging tab favicons. It feels like you're literally saving the tab for later, and it behaves exactly like that, unlike normal bookmarks which use whatever global session state you currently have. In Stainless, the bookmark will always bring you to the same page. Elsewhere, a bookmark will take you to the page only if your current user can see it, possibly showing an error, making you log out of your current account....
Honestly, this is one of the few real new-things I've seen in bookmarks/browsing, and I really grew to like it. It's a far nicer experience.
I wander how was the UX, when would you decide to create a new "session"?