My girlfriend has been having this issue with her S4 mini for a few days. We even went in to the Sprint store to have them look at it. We were told it is a "Samsung issue". Which boggles my mind that it could be the hardware manufacturer causing the issue. However, I use a Nexus 5, and my time is correct. So, it could be how the manufacturer implements their time/date functions. I would hope that the manufacturer wouldn't tinker with such a core piece of functionality within the Android source code, but at this point it wouldn't surprise me.
Furthermore, I used to have a Samsung S3 before I upgraded last year, and I do recall a few times having an issue similar to this with my phone.
We are in Mechanicsburg, which is very close to Harrisburg/Hershey area where the others have reported this. My gut feeling is that this has to be a tower/network issue. However, seeing that all of the people reporting the issue thus far are using Samsung phones, perhaps it is a manufacturer issue.