Certain other nonrefundable credits are indeed applied first, those present on Schedule 3 lines 1 through 3 and Schedule R line 22. If these other credits by themselves are sufficient to reduce your income tax liability to zero, you don't get any Retirement Savings Contributions Credit.
Refundable credits are applied after and are not affected by nonrefundable credits.
For example, someone over age 65 who has an AGI of more than $12,000 but less than $15,525 will get the tax Credit for the Elderly and Disabled on Schedule R first, reducing income tax liability to zero before the application of any Retirement Savings Contributions Credit for which they might otherwise be eligible.
