Once you have had a disaster, just make sure that you do to the "disasters" button (left frame), and then "Plan Relief Resources to recover"... Set evertyhing up so that you have enough to cover both your monthly and your one time needs. That will be used automatically.
Some of the resources, such as tents, are used temporarily, but not consumed, so you dont see anything happen, but if you have them, they are working. Other quantities, like food units, are actually consumed, so you will see the number automatically decrease each month.