I dont think you can log out a user logged on with Windows Authentication method. That's the drawback with this method. The user session ends only when the browser is closed.
One idea though. Always start a new session in a new browser opened by your code and when the user clicks log out button just close the browser. Since the browser window was opened by the code, there will not be any alert message asking the user if he/she wanted to close the window.
Rules at work:
1) Boss is always right
2) If Boss is wrong; refer rule #1