Applying for Academic position after Phd completion
Talk to your supervisor about how to formalize this role.

Most likely you can get an honorary contract or something similar, which will give you an official affiliation with the university that you can put on your CV.  

Besides putting it on your CV, it will also allow you to use the university affiliation when publishing.

The only barrier I see to this would be visa issues, if you no longer have a right to work or study in the country of the university.  I'm not sure the impact on an unpaid position, but it's possible that this would prevent an honorary contract.  In that case, simply put something less formalized like "collaboration with X on articles based on PhD thesis" I don't think it will cause much of a problem.

Potential employers are worried about gaps where you are doing nothing; as long as you can show you are academically active, even if not in a formal role, I don't think you have to worry.