At the end of a voyage the old skippers would carry the boxed chronometers ashore to get the rates checked and if necessary adjusted. If you want a crystal-controlled timepiece to have a constant rate, keeping the frequency-setting components at a constant temperature will help considerably. Wristwatches worn on the wrist run closer to wrist temperature than room ambient. You could put an insulating cuff over the watch in temperature extremes to help even more.
Larger devices might keep the crystal in an oven of some sort, that kept the crystal at a constant elevated temperature.
The mechanism in such timepieces is comparatively crude and has no effect on timekeeping so long as the clock motor has enough power to move the gears. Timekeeping is done by counting cycles of the crystal circuit, and zapping the motor to rotate half a turn each time a second’s worth of cycles have accumulated. 32,768 is a power of two, so binary dividing circuits can work conveniently with it. A four MHz setup would I presume run at 4,194,304 Hz for the same reason.