He is too young -- and will be for some time yet -- to connect his actions with your reactions and the time outs. Time outs are not effective for kids this young; that's why he goes back and picks up kitty again. He is not doing it to spite you; he's doing it because he does not get that he was put in his crib suddenly because he picked up the kitten. Please don't expect more from him that he can do at his age. You can explain every time "what you did that made mommy put you here" but he just won't connect your words to his actions of even five minutes earlier. Ask your pediatrician -- kids his age aren't developmentally ready to do that yet. And it's not his fault, just his age and stage.
You're right: Your instinct is telling you that he is confused about the nature of the time outs. He does not understand the concept; he only knows "I'm somewhere I don't want to be" but does not follow that with "I'm somewhere I don't want to be BECAUSE of my behavior." That leap is a long way off for him.
Like another poster said, keep him away from the kitten. Period. Avoidance is really your only option here to stop him from accidentally hurting the kitten or the kitten from hurting him. I'd stop the time outs because they only frustrate both of you, do not change his behavior, and will make him associate his crib with Bad Things. Soon he'll start resisting going into his crib at bedtime and naptime because he'll see it as a place he is whisked into against his will, alone, at what seem (to him) to be sudden, random times.
I am a cat lover, and I hate to say it but it might be a better option overall to find another loving home for this kitten and get a kitten when you son is old enough to understand how to handle it properly and safely. Kittens are much, much easier to "re-home" than mature cats so you should be able to find a home for this one, I'd hope. I know it seems harsh, but the only other option for probably the next year would seem to be keeping the kitten and your son apart, and in that time the kitten would learn that your son was someone it wasn't supposed to get near -- meaning that later, the grown cat will probably not be affectionate with your son.