a real world point of view
Production associates are people tied to the production team who do not have an industry-standard job description. In the Doctor Who franchise they were specific only to the John Nathan-Turner producership, or, more precisely, those serials between Logopolis and Survival, inclusive. No former production associate is known to have given an interview about their responsibilities. Because of these factors, it is difficult to speak with precision about what a production associate did.
Some sources — including the BBC's official website for the original run of Doctor Who — have mistakenly considered production associates as synonymous with production managers. This, however, is instantly disproved by the credits to, amongst others, Castrovalva and Black Orchid, which firmly credit both titles. On the basis of the credits to, say, Warriors of the Deep, they can be assumed to rank somewhere between an production assistant and a production manager.