I have 4 phones on my plan - 1 LTE & 3 WiMax. It's only the WiMax phones that are doing this (and have been for several months).
I contacted tech support, thinking it was localized problem (I thought maybe it was just one of my local towers). They had a tech look at the issue and it seemed solved for a few days, then it came back.
The fact that my 3 WiMax phones were doing it but my LTE phone was not was a strong indicator that it's the WiMax network. If you people are having the issue on your HTC One, then my assumption about WiMax was wrong.
So far, I've had no timezone issues on my One.