My guess: it is a relatively safe compound with the right properties to act as a working fluid for this movement. The text linked below mentions the working fluid and the property that the vapor pressure is highly variable over the range of normal room temperatures.

Here is a document with details and history about these clocks: https://www.physics.rutgers.edu/~matilsky/documents/Atmos/At...

Professionals have instruments that measure the precise period of the clock ticks that are heard, so the adjustment lever can be set accurately immediately.

With a computer (or with a smartphone), one could easily improvise an equivalent instrument, by recording the ticks with the microphone and displaying the tick period during adjustment.

I take it she lives in a blessedly DST-free jurisdiction, then?