Suppose you're in a car and stomp on the brakes. If you're not wearing a seat belt you'd describe your motion as "thrown forward," but that's an illusion due to the non-inertial reference frame of the accelerating car. To an observer on the side of the road, you're moving forward with the same velocity you had before, while the car around you slows down, so that you catch up with the front windshield.
If you're wearing a seat belt, you still have that "thrown forward" sensation, but now you accelerate with the car. In that case the force you're feeling is the normal force from the seat belt, which is pushing you towards the back of the car. Your intuition gets the direction of the force wrong because of the accelerating reference frame.
It's the same on the rotor ride where the room spins and you stick to the wall. If not for the wall, you'd move in a straight line and leave the ride. The force you feel is the normal force from the wall pushing you inward; your intuition about the direction is incorrect because you're in an accelerating reference frame.