It has its own timescale, but that still traces back to NIST.

In particular, the atomic clocks on board the GPS satellites are not sufficient to maintain a time standard because of relativistic variations and Doppler effects, both of which can be corrected, but only if the exact orbit is known to within exceeding tight tolerances. Those orbital elements are created by reference to NIST. Essentially, the satellite motions are computed using inverse GPS and then we use normal GPS based on those values.