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.