The first indication the reader gets that a lot of time has passed for the Tuck family are these lines from chapter 6:

"We ought to've had some better plan than this," said Miles.

"That's the truth," said Mae helplessly. "The dear Lord knows there's been time enough to think of one, and it had to happen sooner or later.

Mae admits that there has been plenty of time to come up with a better plan about the spring's discovery. It's an important detail to give readers, because it helps the reader realize that Jesse might not have been lying when he told Winnie that he was over a century old.  

Chapter 7 is much more overt about the passage of time. The reason is that chapter 7 is when the Tuck family tells Winnie that they are immortals. They flat out tell her that 87 years have passed. They give a bunch of examples of how they can't be killed, and then the Tucks tell Winnie what really convinced them of their unique lot in life.  

"But it was the passage of time that worried them most. They had worked the farm, settled down, made friends. But after ten years, then twenty, they had to face the fact that there was something terribly wrong. None of them was getting any older."

Miles tells Winnie that he was forty years old and didn't look a day older than his children. All of those details are important, because the reader learns that the Tuck family is not only immortal, but also that their entire aging and maturation process has been halted completely.