If there is an active connection to AirDroid, the URL and Passcode section is replaced with a Disconnect button fairly quickly. And when the browser tab is closed, disconnecting from the device, the URLs and a new Passcode pop up after just a moment.
I didn't know about AirDroid before a few days ago, and therefore never saw the Exit button in the previous version; however, the standard Android exit action is to press the global back button (usually from the application's home/default screen). I personally don't think that there needs to be an exit button in the main window (would likely make if feel cluttered to me). I do think that a nice enhancement would be to add a disconnect and/or exit button to the notification to quickly manage AirDroid if you no longer have the application center stage.