The Tuck family describes their discovery of the spring's magical powers in chapter 7.  They passed and drank from the spring without knowing anything had happened.  The Tuck family eventually found where they were going to settle and began building their homes.  That's when they started to notice that not everything was entirely normal anymore.  

"That was the first time we figured there was something peculiar," said Mae. "Jesse fell out of a tree . . ."

"I was way up in the middle," Jesse interrupted, "trying to saw off some of the big branches before we cut her down. I lost my balance and I fell. . ."

"He landed plum on his head," said Mae with a shudder. "We thought for sure he'd broke his neck. But come to find out, it didn't hurt him a bit!"

As the text indicates, Jesse fell out of a tree and landed on his head.  Normally, such a fall would cave in somebody's skull or break their neck.  Regardless, Jesse should have died, but he was no worse for the wear.  The strange happenings continued to the Tuck family.  

Angus Tuck was bitten by a snake, Miles was shot, and Jesse ate poisonous food.  In each case, nothing happened.  But the big clue to the Tuck family was their lack of maturing and aging.  

"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.

It was then that the Tuck family knew something was wrong.  They were forced to flee the area.  Eventually, the Tuck family happened to return to the spring and realized that the tree and surrounding foliage hadn't changed either.  

That tree hadn't grown one whit in all that time. It was exactly the same. . . So they decided at last that the source of their changelessness was the spring.

Like anything that the spring fed, the Tuck family had become locked into being changeless.