Every time you rescue, there is a chance at getting an item or a pair. Additionally, it lowers the cooldown for watering and fusing.

Suppose the following:

Go to sleep Rescue cooldown finishes Wake up
Time 00:00 01:00 07:00

If you don’t do anything, you’ll rescue once at 07:00. That is 1 roll only, and you will end up with 1 animal.

If you release an animal, you can rescue right away. Then at 07:00, you can rescue again. That is 2 rolls, and you will still end up with 1 animal. However, that additional roll gives you a chance at getting an item or a pair, and also lowering your cooldown for watering and fusing.