Price's Timer is accurate, actually. Server time is inaccurate. I know that on Ruairi, the time changes up to six hours from Channel 1 to Channel 7. Other channels have similar lack of synchronization, and it appears that the same lack is felt from server to server.
However, in most cases, Price will appear at the timer's listed spot shortly after he is scheduled to appear (Price changes location every 36 real life minutes, at in-game midnight). Just check your channel's time. If it isn't midnight yet, he'll appear in the timer's spot then.