So you set your clock up by telling it its own location, so it can offset for the signal's flight time?

No, you tell it the location of multiple towers it receives signals from, then it can compute the unique solution x, y, z, t

But the comment several levels up said they were demoing time with a single tower.

You can get time with a single tower, but not location.

How do you know time of flight for the signal? Tower sends its coordinates, client uses GPS?

Perhaps they were just hand-fed to demonstrate accuracy. If instead of PPS it gave a 10Mhz reference, then there is a pretty good use in keeping nearby systems sample-synchronized. In which case you don't care about 'time' just about frequency accuracy.

The satellites are on known positions too, once you know the time.