"With their plans on building a home 10k(14k us) doesn't go far "
Would it surprise anyone to find out that the 120k is definitely going to go $120k farther than what they had before winning? Or that the vast majority of people who own vacation homes, whether they're in the Caribbean or elsewhere, didn't pay any part of the cost with lottery winnings? Or that an awful lot of people who own vacation homes use them as an investment by renting them to vacationers who don't own a home there.
None of us know what their overall financial situation is, and other than buying/building a vacation home none of us know what their overall plan is. What we know is that they're getting an extra 120k to do what they want to do.