To answer your question, when my hair first dries it's a little stiff and stringy. This is fine because it means my curls have set. What I do is comb my hair in the morning of a day off when I don't have much planned. I let it dry all day. At night I put it back in a braid, and by morning the curls are soft and defined. But while it's drying with the conditioner in it, there isn't much you can do until it dries. Sometimes I wear a smooth headband to keep it back and out of my face while it dries and I run errands.

If you are needing to have "showcase" hair the same day of combing, this will take some planning. Give your hair time to totally dry (or in an emergency, use a diffuser, but only do this occasionally). Then, when it's dry, you could pull your hair back in a bun or a braid and wear it like that for an hour or so (you'll have to experiment on this one). The unbun or unbraid, and it should be soft. If not, do it again. I think it's a matter of gently shifting the hair slightly that eliminates the initial stiffness, so this should do the trick.

Depending on how much control you need in your hair, you could also rinse out most of the conditioner after defining your curls, or use a lighter combing conditioner. These tend to dry less stiff at the beginning (but know that your ends may puff a bit by the next day because they didn't "set" as they would if they had dried stiffer or stringier.)