Thanks for reporting this issue! Organizations are currently only synchronized with the Grafana service when an access token is created/updated (every 2 hours), so there is an unfortunate delay if you add an org while already signed into Grafana. We should be able to handle this edge-case better with a bit of work.
A sign-out link in Grafana is also still in the works, hitting the logout url manually is just a workaround until then.