The urgency has a specific job: it prevents verification, not thought.
People assume pressure is there to stop you thinking clearly. It is more precise than that. Every version of this scam contains a reason you cannot use the one channel that would end it — the phone is broken, they are in a meeting, they are abroad, the app is locked. That constraint is not decoration, it is the entire mechanism. Remove it and the scam collapses in ten seconds, because you would simply ring your child.
So when you are teaching the family what to look for, the signal is not "they asked for money" and not "they were in a hurry". It is: something in the story explains why you cannot check. That is the tell, and it is present in every variant — the courier one, the bank-fraud-department one, the boss-needs-gift-cards one.
Once you name it that way, people spot it themselves in formats they have never seen before.