If you are wondering why you need to log off twice before you noticed any changes to the Group Policies. It is because the Fast Logon Optimization feature is enabled. This is enabled by default to provide faster logon to the system. Without this, a computer will need to contact a domain controller every time when the computer starts, and if there are network issue, the user will not be able to log into their computer. So it is a good idea to leave this feature on. This way the user can use the cache credential to log on.
If you are interested in disabling this feature, here is how you can do it. You will need to modify the Group Policy.
Computer Configuration\Administrative Templates\System\Logon\ Always wait for the network at computer startup and logon