"With jackpots hitting hundreds of millions of dollars" <--- Because people can win $2,000,000 or more from the lottery, "many lottery winners suddenly find themselves with much more money than they're used to" <-----Many people who win the lottery suddenly have much more money than they usually have. From this you can guess: Many people who win the lottery don't know how to handle the money wisely.

"with jackpots hitting hundreds of millions of dollars..." is the same as saying "because/since jackpots are hitting hundreds of millions of dollars ..."

"with jackpots hitting hundreds of millions of dollars" = 'since prizes are as big as hundreds of millions of dollars"

when --> with