The time source I use to verify time on my watches is:
http://www.time.gov/timezone.cgi?Eastern/d/-5/java
This is the official US government site for time.
From what I understand, this site is also the sync source for all Atomic/Radio/NETWORK controlled devices is the US.
If a "RADIO CONTROLLED" watch/clock/device is off by as much as 1 second something is wrong with that individual device. I personally now have three Junghans "Atomic" watches and all sync automatically to this site perfectly - all have the exact time to the second.
As far as the problem synchroserious has pointed out, I am not sure of how that sequence of events is happening as I do not know of a cell phone that displays seconds. Additionally, the time on the cell phone display should be accurate to the minute as the telco's use Stratum Clocks whice are synced to the time source/site I mentioned previously. As a verification experiment, I timed my 4, 2 Sprint 2 Nextel, cell phones against this site and all timed perfectly to the minute change in Denver. (Yes, I do have 4 individual personal cellphones.) Sprint and Nextel have seperate networks here in the states so they do use different devices but they all do track back to the central time source. So it would be interesting to hear more of his story.
FYI - if one DIALS into a "telephone company TIME RECORDING" here in the US chances are that you will hear the wrong time. As an example, if I dial into the phone company site at 11:59AM my Junghans AND the time.gov site are all 7 seconds slow, if I dial in exactly 2 minutes later at 12:01PM the same watches and site are now 7 seconds fast. This happens every day so obviously the telco's voice announcement system is off a little bit.
As an aside, wouldn't it be nice to have a "Atomic"Radio controlled" LED watch? Yeah I know dream on, as right now seconds are even a big problem!!!