Mae and Miles Tuck kidnap Winnie and take her away to their house on a horse.

When Winnie sees Jesse drinking from the spring that made the Tucks immortal, he has to act fast.  He can’t convince her not to drink the spring.  She doesn’t understand why she can’t drink from it.  The only thing they can do is take her home with them so they have more time to explain.

[The] next thing she knew, she was seized and swung through the air, open-mouthed, and found herself straddling the bouncing back of the fat old horse, with Miles and Jesse trotting along on either side, while Mae ran puffing ahead, dragging on the bridle. (Ch. 6)

When the Tucks race by observers, such as the man in the yellow suit, they just say that they are teaching Winnie how to ride a horse.  Winnie is too afraid to say anything.

The Tucks do not want to hurt Winnie.  They are very concerned that Winnie might drink from the spring without realizing the consequences.  They explain to her how they came to realize they were immortal.  Everyone who drank from the spring did not age and did not die in accidents.

The Tucks explain to Winnie what would happen if she drank from the spring.

"We begun to see what it would mean." She peered at Winnie. "Do you understand, child? That water—it stops you right where you are. If you'd had a drink of it today, you'd stay a little girl forever. You'd never grow up, not ever." (Ch. 7)

Winnie gets to know the Tucks and like them.  She especially likes Jesse, but he is a little older than her.  He asks her to drink from the spring when she gets to be his age so that they can be together.  Winnie chooses not to.