When a hurricane rotates, that rotation is very real and occurs in both the inertial and rotating frames. One can think of it from the rotating frame as being due to the Coriolis force.
Let us consider a hurricane in the northern hemisphere.
From the rotating frame:
We have this stationary mass of air. In the center, air is forced upward due to its high temperature and high humidity and the adiabatic lapse rate and all that. The result is like a giant vacuum cleaner sucking air out of the middle. As the air moves toward the middle it is deflected rightward by the Coriolis force. The result is a counter-clockwise torque and a counter-clockwise circulation.
From the inertial frame:
We have this mass of air rotating counter-clockwise along with the surface of the earth. In the center, air is forced upward due to its high temperature and high humidity and the adiabatic lapse rate and all that. The result is like a giant vacuum cleaner sucking air out of the middle. Angular momentum is conserved. The air moving upward in the center carries very little angular momentum away. Air entering from the outskirts adds more. The mass of air in the middle must gain rotation rate as a result. So there is a counter-clockwise circulation. [Or think of it as a twirling skater pulling in her arms]
