Haven't looked into this in depth but sub-nanosecond sync for systems up to 10km apart is interesting since 10km is about 33 light microseconds. There is some trickery going on.
It's totally possible to achieve synchronization better than light transmission time. For the purposes of synchronization, the speed of light delay, and any other delay are indistinguishable, and need not be distinguished.
Two-way time transfer measures the round-trip propagation time. As a result, it's not directly relevant to the accuracy.
The gravity well time dilation is about 3.5 nanoseconds per meter per year near the surface of the earth. (time changes rate with altitude in a gravity well)
Sub-nanosecond synchronization is getting into the relativity is measurable realm.
Yes, it uses phased locked loops and measures phase difference between the master clock and the local clock.
yes, it needs custom built hardware to work.
In our lab tests phase lock jitter between WR client and master is about 10ps (picoseconds) over 50km fiber (with temperature change of the fiber, so WR actively compensates elongations), so relative clock of one system can be transmitted with about that accuracy to another.
P.S. There is WR workshop this week with some talks being publicly available on CERN's indico website.