What you need to know is that a remontoir isolates the watch’s oscillator from the mainspring. What drives the oscillator here is a special constant force hairspring that is fixed to the seconds wheel. The seconds wheel drives the escape wheel, which sends pulses of energy to the anchor. The anchor, in turn, sends this energy to the oscillator. This much is fairly clear, but how does the hairspring on the seconds wheel get rewound every ten seconds?
The answer is pretty simple actually. What happens is that one side of the hairspring is fixed to the seconds wheel, and the other side is fixed to another seconds wheel (lower seconds wheel) that lies directly beneath the first seconds wheel (top seconds wheel). The lower seconds wheel is powered by the mainspring, but because it doesn’t engage the escapement, it is regulated only by a special one-toothed intermediate wheel. This intermediate wheel is locked into place. Every ten seconds, this intermediate wheel is released and allows the lower seconds wheel to revolve just enough to charge the remontoir hairspring with enough energy to drive the top seconds wheel for ten seconds. Once this energy is depleted, the intermediate wheel is released again to recharge the hairspring, and so on.

THE FOUR STEPS TO THE FLOW OF POWER
1) Energy flows from the two huge stacked barrels to the gear train, and then from the gear train to the lower seconds wheel.
2) This wheel is in contact with the pinion of the one-toothed intermediate wheel. The intermediate wheel is locked by a lever, which is in contact with a triangular-shaped cam on the top seconds wheel.
3) This cam acts on the lever to release the intermediate wheel. The intermediate wheel travels 180 degrees simultaneously, allowing the lower seconds wheel to revolve.
4) Because the lower seconds wheel is fixed with one end of the constant force hairspring, which is fixed on the other side to the top seconds wheel, this action winds the hairspring. In other words, the lower seconds wheel is always turning slightly ahead of the top seconds wheel to wind its hairspring.

Label: Top seconds wheel, Lower seconds wheel, One-toothed intermediate wheel, Constant force hairspring, Triangle-shaped cam

ADD IN IMAGE 3 OF TOURBILLON WITH REMONTOIR FROM MISHKA
An image provided by a reader demonstrates that the Remontoir can also be implemented in a tourbillon, according to a Richemont Patent.

pivoting lever

intermediate wheel

triangular-shaped cam

constant force hairspring

top seconds wheel

bottom
seconds wheel

counter weight

intermediate
wheel

lever

triangular-shaped cam

pinion of
intermediate
wheel

top seconds wheel

lower
seconds
wheel

constant force mechanism

constant
force
hairspring