The college will give you your family contribution as they calculate it to be. They do not say who pays what. That is a decision you and your former spouse will need to make.
For CSS Profile Schools, I would say…ignore the FAFSA SAI (which is the new term for EFC). Really, all that number does is give the colleges your eligibility for federally funded grant aid like the Pell (if you are eligible), and allows your student to take the federally funded Direct Loan.
The Profile schools will use the information on your profile and the non-custodial parent profile to determine the family contribution for your student. And they will award need based aid based on the formulas used by each college (and they do vary…and it can be by a lot).
So…you have to wait to see what the college net cost for your student is at each college and then you and your former spouse need to determine how that will be paid. The college does not do that for you.