Classic explanation

What if we have a button on the clocks which have already been arranged in the coordinates and when we click the button all the clocks start at the same time. Hypothetically speaking if we can place so many people at the clocks we could also have a wireless connection between the clocks that make them start altogether or would the signal take some time to reach the clock and they won't be synchronized.

(x, y, z, t)

And then we add gravity and all clocks become unsynchronized!

I'm afraid one goal of this example is to show all the clocks are tied to the their xyz location in space indeed. At least were this working properly. The "time biasing" only cancels the travel time. So the real world net effect is actually as you wrote, they won't be in sync. BR JKi