The coke bottle and egg works because the match burns the air in the bottle, reducing the pressure.
The tire is just like a cylinder in an engine. You have an air-fuel mixture and when you ignite it, it expands (rapidly) and the force pushes outward. In this case it pushes on the inside of the tire forcing it against the bead.
It does not work on vacuum. *if* there was a vacumm in the tire, the pressure on the outside of the tire would push it away from the rim, opposite of what we want.
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