That is an excellent thought experiment to consider for a spinning vehicle. You are correct that if you simply enter the open space inside the rotating cylinder, somehow not following the rotation yourself, you will not experience a force to pull you to the outside. You could just hang there and watch the "floor" rotate below you.
However you probably won't be able to just hang there, assuming that there is air in the space. If you're alive and breathing, then the air will also be moving by you (the boundary effect with the floor and walls will be moving the air around with them), which will start you moving in the same direction as the floor. As it imparts a force in that direction, you will start moving on a trajectory perpendicular to the radius. You will then be on a trajectory to intersect the floor, which is curving up in front of you. As you get closer, the air will be moving faster, further accelerating you to the floor in front of you. It will seem like falling towards, as well as catching up with, the floor.
In what is normally seen in depictions of such a vehicle, you would not float into the space and wait to be directed to the floor by the moving air, but rather you would control your descent on a ladder. (Seems sensible, as opposed to an uncontrolled fall, however slow.) Then you are rotating with the floor, with your angular velocity increasing as you descend, increasing the the apparent weight on your feet on the ladder as you descend.