The "yellow man", or more accurately, the man in the yellow suit has heard about the Tucks from the former wife of Miles, one of the Tuck's sons. This man wants to find the family because he wants to earn immortal life himself. Mae and Angus Tuck attack him and he is killed by a blow to the head.
The reason he must die is because of what he wants (immortal life) and the risk that he will expose the family to others. The assumption is that others will descend upon the family and also demand the secret to immortality. Mae and Angus understand that this "gift" is really a burden. To have immortality is to live a life of boredom. They understand now the value of mortality in having happiness - the fact that life is short allows humans to live it more fully and to appreciate it more.