Depending on the belt used the tires don't actually just "pop" like in the movies. They get holds such causes them to deflate and become undeliverable. Ever got a punctured tire before? It's not an instant process by any means.
There are belts can actually make larger holes as the spike comes out, but this doesn't seem to be the case here.
They usually give the whole "you will be assimilated" spiel beforehand but hard to say if that would be something that the common folks would know or only world leaders