Waiting for them to calm down does not work for my DS either. In fact if you just wait, 9/10 he will get more and more and more wound up. Usually to the point that an adult gets wound up in response. He is only 6 so it's not the same, if necessary we can restrain him so nobody is in danger but it's not a nice thing to do all the same, and we have had to look into how else to calm him down when he starts escalating. (I have a 16yo who had similar behaviours too so that's why I feel a bit more confident this time around - we have been here before.)
I think that again, this is a good example of why the underlying assumption is important.
When a child is kicking off in a supermarket because of a fairly minor thing, like they have learnt from previous behaviour this will get an adult to buy them a toy, then taking them outside and waiting for them to run out of steam is a perfectly reasonable approach and will probably work to begin to change that expectation of the child. I expect that the course leader is also suggesting positive reinforcement for the wanted behaviour in the supermarket too, such as praise for holding hands/sitting quietly in the trolley, or offering them a job to do such as holding a shopping list. All of this is based on the assumption that for the child, grocery shopping and supermarkets is something that they can easily handle and the main issue is that they are bored and impulsive, they do not automatically pick up the social expectations of supermarkets like a NT child would, or because of previous difficult behaviour they have become used to the idea of parents distracting them with a bribe.
For those children the suggestions will probably work and that is the majority of the children whose parents are on the course.
However, if your child is kicking off in a supermarket because the entire environment/experience is overwhelming for them and/or it's too much of an expectation to handle right now, his brain has gone right into protection mode and he is reacting as though there is a threat to his life, because his limbic system is interpreting all this stuff as though there genuinely is a threat to his life.
Taking him outside isn't going to remove his sense of felt threat, because the threat is not tangible. There is nothing physically in the supermarket which is causing this directly. It is (most likely) an overload, a combination - if you have ever played the game Buckaroo, think like that, how each item individually will not trigger the donkey to buck, but once the total weight reaches a certain point, it will all come flying off - those "individual items" could be sensory input, it could be all of the people, it could be having to make multiple decisions about what to buy, it could be the writing on the packaging of all the food and the special offer signs and all of this information which is being bombarded at us in order to make us want to spend money. It could be things that happened earlier in the day or week. Stuart Shanker is good at explaining/breaking this stuff down BTW. He is much more enjoyable to listen to as well but I do find it takes a lot of listening to various things he has done to get the whole picture.
The way that you will help him to calm down in that situation is to find out what, for him, constitutes felt safety. What will provide the opposite signals to his body to calm the alarm and help him realise that he is not under threat. And for you to (somehow, because it's bloody hard!!) calm your own limbic system and keep yourself in "owl brain" territory where you know there is no threat and you are the safety.
The absolute LAST thing that will do this is for you to take him out and berate him and tell him to calm down and now he's lost his sticker or whatever nonsense reward he has been promised. A reward won't provide felt safety. It works for the other children because the other children do not need this extra reassurance. They already feel safe in a supermarket. Your son does not, that's why he is reacting differently. It is not because you're getting it wrong.