Our Windows Updates are installed automatically during the maintenance window, which is configured manually on each of our 2012 R2 servers, so that we can specify different times for each server, or group of servers. Unfortunately, those servers do not automatically reboot after the updates have been installed and I have no idea why!
All of our 2012 R2 servers currently have the status "Online - restart pending" and are coloured red in Server Manager. I would have expected them to have automatically restarted at the scheduled time, since that's how I've configured it via Group Policy.
Windows Update is configured like this: