That is mostly the case. However, other websites may ask your browser to make requests to Facebook domains (to load in social buttons or tracking scripts/pixels). Those requests will include any cookies your browser has for Facebook as they're direct to Facebook domains.
This extension gives Firefox selective amnesia: if you're in a Facebook container tab, it'll remember and send those cookies. If you're not, it won't!
An alternative solution is to never make those third party requests in the first place, but you might need some of them for content you're actually interested in viewing. Using both a blocking extension and this container extension should improve your privacy towards Facebook.
This extension gives Firefox selective amnesia: if you're in a Facebook container tab, it'll remember and send those cookies. If you're not, it won't!
An alternative solution is to never make those third party requests in the first place, but you might need some of them for content you're actually interested in viewing. Using both a blocking extension and this container extension should improve your privacy towards Facebook.