The NCAA pays travel, lodging and per diem for the traveling party of team, staff, cheerleaders and band. By bus if <350 miles from school to regional site and by air if >350 miles.
Right. And then they distribute millions to the conferences. They use a formula that counts all games a conference has been in over the past "N" tournaments (I think N=6, so NU's 2 games will be counted in the B1G total multiple times, this year, next, etc). Obviously, each victory means and extra game, so those conferences that win more, play more, and in the end get more money. The conferences then distribute the money following their own rules. With google, you'll find articles giving greater detail on this, if you need it.