Your writer has a significant fact wrong and botched the explanation of why cyclones do not cross the equator.
First of all, the Coriolis effect is at it maximum at the equator, not zero as stated in the write-up. The force from Coriolis is proportional to (ω X r), where ω is the rotation speed and r is the axial distance from the center of rotation. Since the Earth turns on the axis that runs through the poles, the equator is at the maximum distance from this axis, so it gets the maximum Coriolis forces. Conversely, the polar regions have the least Coriolis forces.
The main reason that cyclones do not cross the equator is due to convection. The Earth's atmosphere has organized itself into a total of six convection zones: the north and south tropic zone, the north and south temperate zone, and the north and south polar zone. For the tropic zones, they start at the equator and nominally extend 30 degree north or south. The convection pattern goes like this: the maximum amount of heating occur at the equator so that air is moving vertically and at the temperate zone the air is coolest, causing the air to sink. For example in the northern tropic zone, as the hot rises it flows north. With Coriolis, this air is "pulled" to the west. The high part of the convention loop is what is know as the steering current. Since Coriolis is at the maximum at the equator, you can note that most of the northern storms start out travelling in a westerly to north-westerly direction.
One other thing I would like to mention, once a northern hemisphere storm hits the temperate zone, they all tend to take a right hand turn, and head in an easterly direction. This is very important to me, since I live in New Orleans, which is at 30 degrees north latitude. I have watched many storms hit Texas boomerang back at us.