do I also need to put this management fee in box 7 "State income" ?
If the person you are issuing the 1099-NIC to is a CA resident, or if the business you are issuing it to is registered as a business in CA, then yes, you need to include what you paid them in box 7 also. Note that you may also be required to send a copy of that form to the CA state also. Where exactly you send it, I don't know. But I would expect the program to inform you of where and how you can send it, when you print the form.