> Most likely the 1st transformer is simply a 1:1 isolation transformer.
I'd bet on something like 120V:24V. It wants to make maybe +/-10% adjustments.
Then the center-tapped variac can apply 120V in-phase or reverse-phase, adding or subtracting 24V from the input voltage, to keep the output voltage "right".
Re-draw like this (below):
> regoulation if input voltage increase but not if it decreases (with an usual variac)
The usual Variac is wound (in the US) with 0V, 120V, and 140V taps. We feed the 0V and 120V taps with fairly constant 120V, we can get from zero to 140V out.
But your regulator does NOT want zero output. If we only use the (US voltage) 100V to 140V range, then 70% of the core must be wound but is never used by the output.
So they use the full 100% range of the variac, and step-down to give 10% add/subtract.
Another trick is the center-tap. The variac could be smaller/cheaper if it only went 0%-100%, and we used a phase-reverse switch to change from boost to buck. However consider the case where output is supposed to be 220V and input is wandering 219V to 221V. That phase-reverse switch would be clacking a lot. And it needs more brains to decide which way the switch should go. You also have to reverse the wires to the motor. So I guess they decided it was simpler to center-tap the variac and let the motor slide smoothly from maximum buck, through no-change, to maximum boost.