Maybe it's both the mother (Neita/Nita) and the person or persons asking the question. "Oh, Cudelia? Why's your head red? Oh, I know! You've been in the sun a lot." That's the person asking the question. The mother says "I met Mr Ivan on a moonshine night". The person teasing her says, or implies, "I met Mr Ivan too, and guess what, he told my parents who told my aunt who mentioned to me he had a relationship with Neita (the mother)". I'm imagining both her and the person singing the song as pretty young- school kids, for some reason. It sounds like that to me, anyway. It would certainly answer the question of why Neita refers to herself in the third person. "Missa Ivan tol' me, sey that he give Neita di drop."
Maybe Gibb Sahib will stop by and comment. After all, he has knowledge of Jamaican songs. He can probably turn up an earlier reference for this one.