My hair is stiff right when it dries, which means the curls are well defined, but like yours it softens up by the next day. I'm not sure how much water you are spraying on the next day, or how much conditioner you are using when you add more, but off the top of my head I'd say maybe just wet your hands, and smooth your wet hands over your hair the next day (no extra conditioner on day one if it was stiff the night before).

Then for the second day, wet your hands, add only about a dime of conditioner, rub together, and smooth over your hair. Repeat as needed.

I think spraying our hair tends to make it puff up just like being in really humid weather. This is because the water is being unevenly distributed, making each hair, and even different sections of the same hair curl differently, so our hair puffs. That's that's why I recommend smoothing our wet hands over curls instead.

And for the second day on up to the day you wash it, you really don't need much conditioner. Wetting your hands and smoothing it over your curls should go a long way.