Suppose a car is negotiating a bend on a smooth road and it starts to slip away. What is the force acting on the car causing it to slip away? I know that the centrifugal force is fictitious. Since the road is smooth, we can neglect the centripetal force created by the friction. So what causes the slipping of the car if the centrifugal force is fictitious?
Newton's first law: a body in motion stays in motion in a straight line unless acted on by a force. A car going around a curve wants to go straight under its own inertia. Only the centripetal force inward by the road on the tires (through friction) causes it to turn. Remove the friction and there's no centripetal force, and the car goes straight - off the curve.
Similarly, the people's bodies in the car want to go straight (off the curve). The friction between them and the seats and seat-belts, or the doors pushes them out of their straight, intertial path around the curve. You feel that as a centrifugal force (which is not fiction in the frame of reference of the occupants).