Just to clarify, if the second is mainly syrup from the feeding do not put the super on until you see brood. The reason why is they will promptly move the syrup into the super to clear nest space. When you harvest your honey later, it will be ?adultered?, with syrup in it. By waiting for brood, the intent is they will consume the syrup frames to feed the brood, thus avoiding the honey problem.
If they need space, remove a few to 3 heavy frames from the second, save for feeding at dearth or winter preps. Replace with those empty frames. Wait for larvae. Then add super.