How did the Tucks know that the spring water made them immortal in Tuck Everlasting?

The Tucks became aware that the spring water made them immortal when they did not die of life-threatening injuries.

When the Tuck family first drank from the forest spring, they had no idea what effect it would have.  However, they soon noticed some strange things.  They entire family drank from the spring, and so did their horse.  Their cat did not drink from the spring, however, and this became the key to identifying the source...

The Tucks became aware that the spring water made them immortal when they did not die of life-threatening injuries.

When the Tuck family first drank from the forest spring, they had no idea what effect it would have.  However, they soon noticed some strange things.  They entire family drank from the spring, and so did their horse.  Their cat did not drink from the spring, however, and this became the key to identifying the source of their immortality.  The humans and the horse did not die, even when they should have, but the cat only lived out its natural life.

The family shares with Winnie some of the mortal encounters they had.  First, Jesse fell out of a tree and didn’t get hurt when he should have.  Then, something really strange happened with the horse.

"Not long after," Miles went on, "some hunters come by one day at sunset. The horse was out grazing by some trees and they shot him. Mistook him for a deer, they said. Can you fancy that? But the thing is, they didn't kill him. The bullet went right on through him, and didn't hardly even leave a mark." (Ch. 7)

Other unusual incidents include Pa getting a snakebite, Jesse eating poisonous mushrooms, and Ma cutting herself with a knife.  They were supposed to die, but they didn’t because they drank from the spring.  More importantly, no one was aging either.  Miles’s family stayed the age they were, and he didn’t. 

"I was more'n forty by then," said Miles sadly. "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

This is a trend that would follow the family.  They could not stay in one place without attracting attention, because people would wonder why they weren’t aging.  As a result, the family became nomadic and lived on the outskirts of towns.

All of this information underscores the reasons why Jesse could not let Winnie drink from the spring.  While being immortal sounds good, it is actually quite a lonely life.  The Tucks drank without knowing what would happen.  Jesse wanted to make sure that the same thing did not happen to young Winnie.