I am getting this same exact problem. Also, even after I change the setting to "Automatic date & time" occaisionally my date and time will change back and forth to the incorrect date and time. To stop this from happening I disabled "Automatic date & time" but then every time I reboot it changes to to wrong date and time again. It's like it is not being saved between boots for some reason.
Sprint Galaxy Note 3 Black
HTC G1 Dream ---> (iPhone phase) ---> HTC EVO3D ---> Galaxy S3 ---> Galaxy Note 3