Gravity in an O'Neill Cylinder

So I was recently re-reading Rendezvous with Rama, and it got me thinking.

In the book, they enter at the center of the tube and are therefore in effectively zero gravity. However as they climb down gravity rises eventually massing out at about .5g on the inside surface of the cylinder..

Now, this increase as they're walking down the stairs I get. What I'm thinking is wrong is the scene where the one crewman is flying, and he lowers himself down some to take advantage of the higher gravity.

It got me to thinking, gravity is simulated in a spinning station by the use of centrifugal force, which is what Rama uses in the book. So as you stand on the surface (inside outer wall) what feels like gravity is actually the radial acceleration of the spinning tube forcing you to change direction as it rotates. This would also apply to climbing down the stairs which is why that part makes sense.

However, floating or flying down you should really be in zero gravity the whole time until you reach the surface. Then it wouldn't be the "gravity and fall" that hurts but the fact that the ground should be rushing past you at a very fast speed. In fact your vertical speed wouldn't increase at all, as actual gravity doesn't actually play a factor here.

Come to think of it, one of these cylinders should also have pretty strong winds at all times as a result of the Coriolis forces in play.

Am I missing something here or am I actually seeing this correctly? Cause as i think of it, I see this in other sci-fi in similar settings.