Will his sister overstaying be a problem for his parents’ tourist visa case?

It should not affect the parents being able to get immigrant visas.

For a tourist visa, one does not technically have a "sponsor." However, the consulate will look to where family is to determine likelihood of a return to the home country, so her overstay will be a factor in approving or denying a visitor visa.

What do you mean by "sponsor". Did he invite his sister to visit? Is he inviting now his parents to visit or is he sponsoring them for permanent residency (i.e., "petitioning" them). If he is petitioning for his parents, I don't see how their immigrant visas will be denied because their daughter overstayed in the U.S. If they seek only to visit, then, yes, the consulate may use their daughter's violation against them as they consider all other factors too.