Spinning heads
What student or pilot is going to inadvertently place the aircraft inverted leading into a spin as described ! I assure you it will never happen. However;
1) You must be able to demonstrate and breakdown into small elements the entry into the spin in order to educate the student with the likely factors that may lead to an in-advertant spin.
2) the student must be given time within the spin to identify it correctly but following through your instruction.
3) the student must understand the particular recovery action for their aircraft. The standard spin recovery actions will work however on most if not all aircraft although it should be stressed that it is not always the best method given a particular type. Following your demo, repeat to allow the student to undertake the recovery themselves. (handing over)
Never yank the control column full aft leaving the nose precariously pointing at the heavens followed by a boot full of rudder for that is nonsense. The student will simply end up in neverland and from it learn zilt other than fear! It is not necessary to scare anyone that way.
One method is to maintain some power and bring the aircraft slowly toward the stall condition. Prior to the stall apply rudder fully BUT smoothly, maintain and then, and only then, with yaw achieved apply full back pressure (a sudden jolt is not necessary). The aircraft will quicken in rotation and enter the spin. That is about as close as you can get in simulating the un-intended spin, which is the real concern. The symtoms and aircaft characteristics of the spin should then be identified and the correct recovery taught BUT always involving the student. They should not be scared anymore than they already may be!
Like it or not the fully developed spin and recovery is still part of the PPL syllabus although not mandatory and as an instructor it should be within your competance. Choose or not whether you will ever teach it once qualified.