A contingency is money set aside to reduce the impact of unexpected events and repairs. If your contractor is a smart, well-seasoned contractor, then they know to plan for the unexpected.
If your contractor has a contingency in your budget and you need to access those funds you will need to produce a paid receipt for those items that were not in your original budget or for those items that cost, you more than you had budgeted for.
You will also need a letter of explanation of why you need those contingency funds. If you don’t use those funds during the rehab, those funds will be released on the last disbursement when the rehab is completed.