Session doesn't end when browser window is closed

I am building an application that involves a registration form. If I log in, start to fill out the registration form and submit, I get the validation errors that I would expect. But if I then close the browser window, and then go back to the application, I get the login screen but with the previous validation error messages still showing above the login form, and I get the navigation tabs that belonged to the logged in user, including a logout tab.

Why is the session not ending when the browser window is closed?