[jjoonathan]

Right. Actually, from what I understand, the situation is even more dire and Cesium clocks are (would be) complete rubbish at timing consecutive ticks, so when people say cesium clock they actually mean a quartz oscillator (ultrapure, double ovenized, binned, aged, etc -- but still quartz) to create the output and then a control loop to push/pull the quartz oscillator and frequency lock it to the cesium absorption line.

A similar trick is more commonly used to lock, say, a 5.8GHz on-chip oscillator to a 10MHz quartz oscillator, except in this case the quartz oscillator plays the role of long-term reference and the on-chip VCO plays the role of short-term reference, whereas in the case of an atomic clock it's the other way around.

The overall game is that different filters/oscillators are better at different timescales, so you use control loops to synthesize the best parts of each of them into a clock that is good at all timescales.