Why does Winnie think she is being kidnapped?

Winnie believes that she is being kidnapped in chapter 6 because she is physically picked up from the ground, deposited onto the back of a horse, and rushed out of the area where she and Jesse have just been talking. All of this happens without her permission. In fact, Winnie isn't even given the opportunity to say no. Jesse, Miles, and Mae simply decide that they need to take Winnie with them.

First she was kneeling on the ground, insisting on a drink from the spring, and 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.

As it turns out, though, the Tucks are just as frightened as Winnie.

Winnie had often been haunted by visions of what it would be like to be kidnapped. But none of her visions had been like this, with her kidnappers just as alarmed as she was herself. She had always pictured a troupe of burly men with long black mustaches who would tumble her into a blanket and bear her off like a sack of potatoes while she pleaded for mercy. But, instead, it was they, Mae Tuck and Miles and Jesse, who were pleading.

The reason for the Tucks' fright is because Winnie discovers their secret spring, and the Tucks panic as to how to respond. Their panicked response is to grab Winnie and get her away from the spring. Once Winnie is away from the spring, the Tucks then explain to Winnie who they are and what the spring is capable of doing.