Here's a description of the duties of a Public Affairs Officer:
http://www.todaysmilitary.com/careers-benefits/careers/public-affairs-officers
Now the above description is for an actual officer, and while JD Vance was only a corporal, this means that technically he wasn't actually a Public Affairs Officer, but rather was an enlisted man working in the Public Affairs office, so his duties would be even less than what's listed in the above link, with even less responsibility.