The Tucks became immortal in around 1793.
The book takes place in 1880 and 1881. The Tucks drank from the spring 87 years before. After Winnie accidentally sees Jeese drinking from the spring in the woods outside her house, he takes her to his family (kidnapping her) and they tell her what happened.
Eighty-seven years before, the Tucks had come from a long way to the east, looking for a place to settle. In those days the wood was not a wood, it was a forest, just as her grandmother had said: a forest that went on and on and on. (Ch. 7)
The Tucks all drank from the spring accidentally, and after some time they all realized that they were immortal. After that, they had a little bit of trouble adjusting. It was especially hard for the boys, because Miles had a family that grew old without him (and his wife did not understand) and Jesse did not have the opportunity to have one. The situation with Miles is a good example of the difficulty of having a family when you are immortal and they are not.
"I was married. I had two children. But, from the look of me, I was still twenty-two. My wife, she finally made up her mind I'd sold my soul to the Devil. She left me. She went away and she took the children with her." (Ch. 7)
Jesse asks Winnie to drink from the spring water when she is seventeen, which is seven years after the story takes place, so that she can become immortal and they can be together. He asks her this because he is lonely, and he likes her. However, when Ma and Pa go back, it is 1950, and Winnie has been dead two years. Pa is happy for her though, because she got to have a life, and be a wife and mother (according to her headstone).
One of the things that this story tells us is that being immortal is hard. The Tucks did not choose to become immortal, but once they are, they try their best to make sure that no one else makes the same mistake that they did because they understand the danger of being stuck in life without really being a part of it.