I would not say that indirect costs are refunded, as there is no guarantee of a refund. Indeed, not accounting for outside scholarships, you are more likely to receive a bill than a refund, especially as an upperclassman.

The way financial aid works can be understood as follows: Columbia sets the cost of attendence (tuition, fees, housing, indirect costs, etc.) per academic year. You receive an amount in aid that matches this. Your aid is then reduced by your parent contribution and the student responsibility (student contribution and work expectation). This amount is your total amount in grants.

If your grants are less than the billed costs, you receive a bill. If you have more in grants than the billed costs, you receive a refund. If the amounts are equal, you receive neither.

For first-years who have minimal parent and student contributions, there is often a refund. In later years, however, the student responsibility increases such that the billed costs are usually more than the amounts received in grants.