Integrated Windows Authentication is enabled on the Exchange virtual directory (OWA) by default. With Integrated Windows Authentication, when a user with a domain user account logs onto the domain from a domain joined computer and accesses OWA, the user is not prompted for credentials, which is the purpose behind using Integrated Windows Authentication.
If you can't control the orderly log off of the Kiosk computers when users are finished using them, then you can disable Integrated Windows Authentication on the Exchange virtual directory.
Another solution would be to unjoin the Kiosk computers from the domain and create a local user account on the Kiosk computers that everyone will use to log onto the Kiosk computer (they won't be logging on to the domain at this point) which will then neccessitate them providing their domain username and password when accessing OWA from the Kiosk computers.