CS has excellent ROI at most schools… Especially top 50+ (some colleges are very strong in CS rankings but may not rank as high generally). You are not going to get a better ROI paying 50K or more at a T25 vs 35K or less at a “mid tier” school - so keep that in mind. Not worth spending an extra 20k+ per year for the more prestigious college. Especially if you don’t have at (are there other kids??)
Re: testing. Don’t rely on the tutor entirely. Have him do strictly timed sections at home. ACT releases 2 tests a year. Print them off from the internet and have him sit for the 1 hour math section with the calculator and strict testing conditions. Rinse and repeat. The tutor should be used for strategy and to help him figure out why he choose the wrong answer. Then take it again. Repeat ?