Question: am I right in thinking that the way these things work is by
supplying a tiny bit more air to the throttle body and thus "fooling" the
ECU into "thinking" that the engine is running faster and thus supplying
more fuel? If not, how do these things work?

So many mysteries.

Good news that someone is supplying remanufactured parts. Otherwise we'd all
have to learn some lessons from the Cubans. Maybe not such a bad thing, come
to think of it.