Based on this NSA documentation [1], they didn't actually synchronise the clocks with each other. They just tuned each machine's quartz oscillator with the nearest national time source. They were mostly dialling in the oscillator frequency here, not the exact time, so it didn't really matter they were synchronising to different national time standards.

Besides, even with the automated start system, the actual spin-up time of the turntables would have been a little chaotic. I suspect they were only aiming to get the four turntables within about 100ms of each other. The decrypted signal itself could then be used for the final fine-tuning of the timings (which also included adjusting for any speed-of-light delays)

If you weren't within 20ms, the operator would only hear noise (like a radio). Once they were within ~20ms, the operator would start hearing silence and would tune the phase until all noise went away.

You don't really need exact synchronisation because like a radio, the operator could just scrub the tuning to find the silence.

The synchronised clocks meant that once the operators had locked on, it would stay locked for a long time.

[1] https://www.nsa.gov/portals/75/documents/about/cryptologic-h...