Dino Chase!; Dinosaur Time, by Michael Foreman (London: Andersen Press, 2002).

Tom's mother buys a new egg timer which looks like a saucer and tells him "This is not a toy, don't play with it". But he can't resist and in his hands it starts to wink, and the world spins round and he finds himself in a world of dinosaurs who chase him. He falls into a next and off a cliff and finally stops still long enough to use the timer, when he finds he has brought an egg with him and it's hatched, and is stuck in a bucket so he sticks the timer on the bucket and sends the little dinosaur home, and its mother looks at the timer and says, "This is not a toy, don't play with it". But he can't resist and in his hands it starts to wink, and the world spins round and he finds himself.......

And yes, it does feel that whirlwind.