I don't see the problem. Yes, you are not allowed to distribute the files, but there is no difference between the guy remote coding, or local coding. Either way it is your non-public test-setup. So within the license agreement.
The risk is 100% yours. If your licensed files are distributed by him, not he, but YOU are legally responsible for that, and you Will be hold responsible. I hope since it's a paid job that you have a written and signed contract with the developer(s).
There's no difference in my opinion if the files and host account is on your computer, your host computer, or your developers' setup. He needs access to the files to read the code, customize it, upload new files and work with the instance to develop something.
That said: He's not much of a developer if he writes code for others without having invested in a license himself so he doesn't NEED the license of the other party. That way he is more professional, and he doesn't put the owner of the license in the position you're in.