It might be time to bring in a meteorologist on this one. It certainly goes well beyond my own knowledge of hurricane physics. And so, the following would have to be considered speculation on my part.

If a hurricane spins in a clockwise direction then when it hits land to the north its wind will drag that land to the east. But at the same time the south end of the hurricane will be dragging ocean water to the west. And outside the hurricane area, air will be spinning in a counterclockwise direction with a force equal to the force of the clockwise spinning air within the hurricane.

As a result the hurricane would produce a clockwise twisting effect on the Earth's crust below it. However, over the entire surface of the Earth all of those forces would cancel one another. And the Earth would not change its rotation speed.

On the other hand, if the land and water near the equator were pressed towards the center of the Earth then its rotation speed would increase. And if they moved farther out into space its rotation speed would decrease. The spinning motion of the hurricane and the warm air and water beneath it create a vacuum beneath the hurricane (I suspect). That then causes land and water in the area to be drawn upward and away from the center of the Earth. If enough mass were involved then that might slow the Earth's rotation speed. Then when the hurricane ended and that bulge disappeared the Earth's rotation speed would return to normal.

Once again, that is mostly speculation on my part.

Whatever the case, the theory that hurricane wind induced movement of a continent might add sufficient temporary or permanent strain to some of its fault zones and cause earthquakes to occur sounds reasonable to me.