Is There a Difference Between IIT and Global Works?

First order theories would in short say that you don't need to be aware of the internal workings of your mind in order to be conscious. So then, and you do the want to do the same kind of thing like in split brain cases, say, well, right side of the brain has high phi, so it's conscious. So, my question is, isn't there a problem here with that? I think this question is related to global works especially.