Yes you are correct. The question is a bad one. It does not state that normal reaction disappears also. It would continue to act, if only for a short time (while contact continues), but without gravity it would propel the person away from the Earth. (The contact force would only disappear if the electrostatic force stopped, but that would be catastrophic because that is the force which holds atoms and molecules together, and also keeps them apart.)
If the person were balanced on a spring there is no question that the spring would continue to push him up when the force which holds him down (his weight) is removed. The same is true for wooden and even concrete floors. They also deform like very stiff springs. If the force which compresses them is removed (ie the person's weight) the force which they exert is unbalanced and pushes the person up.
I assume that gravity is switched off instantaneously. If it is switched off gradually then the forces on the person are balanced at every instant. This is a quasi-static process, and probably takes only a small (but finite) fraction of a second. The person does not gain any kinetic energy and does not fly up when the contact force becomes zero.
Adhesion forces (such as Van der Waals forces) would continue to act if the person remains in contact with the ground. These are usually much smaller than the weight of the person, and depend on contact area. They would not prevent him from being projected into space, but they might keep him from drifting away.