The man in the yellow suit is following Winnie and the Tucks to find the spring that grants immorality.
Winnie spoke to the man in the yellow suit at her house. He asked her how long her family had lived near the woods and said he was looking for "a family." Her grandmother came out, and they heard music from the woods. (It was Mae Tuck's music box.) Winnie’s grandmother thought it was elves, and the man in the yellow suit was excited to learn that she had heard it before. He felt he was in the right spot.
Later, Winnie was in the woods when she saw Jesse Tuck drink from the spring. She wanted to drink too, because she was thirsty. Jesse and his mother kidnapped her, because they could not let her drink and accidentally become immortal. They wanted to explain things to her later.
As they were racing away on the horse, Winnie saw the man in the yellow suit.
Discovering him, seeing his surprise, and presented at once with choices, Winnie's mind perversely went blank. Instead of crying out for help, she merely goggled at him as they fled past the spot where he stood. (Ch. 6)
Winnie felt that since she was being kidnapped she should do something. Mae Tuck told the man in the yellow suit that they were teaching their little girl how to ride. She had no idea that he was looking for the Tuck family. Of course, the man in the yellow suit knew who Winnie was and where she lived, but the Tucks did not know that.
The man in the yellow suit’s objective was to find the spring and make money off of it. The Tucks had kept it a secret for years. They did not want anyone else to become immortal, because they had become immortal by accident and they felt it was unnatural.
The man in the yellow suit was able to follow them to the Tuck's house eventually. By that time, the Tucks had already told Winnie about the spring. They were horrified that the man in the yellow suit wanted to sell the spring water. He also said he would have Winnie drink some and be his demonstration. At this, Mae Tuck hit him with a shotgun, killing him. The constable finally arrived, and arrested her.