The answer to this question can be found in chapter 22 of Tuck Everlasting. Winnie is back at home, and she is quite bored. The chapter begins with her trying to occupy her time outside of the house. Her family is worried about her and would like her to stay inside, but her family also realizes that they need to give her a little bit of space. The day is extremely hot, and Winnie is trying to think of a way to help Mae get out of jail. Suddenly, she finds that Jesse Tuck is just outside the fence. He has come to see Winnie for a few reasons. He directly states that he has come to say goodbye:
Anyhow, I come to say goodbye.
A second reason for Jesse's visit is to give Winnie a little bottle of the magical spring water. He tells Winnie that she can drink it around the time that she is seventeen years old. Then she can come and find the Tuck family. He isn't sure how that will happen, but he says that his family will somehow leave her directions.
Jesse also fills in Winnie about the current plan to break Mae out of jail. He tells Winnie that Miles will use his carpentry skills to take the window frame right out of the jail wall. Mae can then escape. Winnie offers to help with the plan by taking Mae's spot in order to fool the constable for a little bit longer and give the Tuck family more time to escape.