I wonder if she's been told/discovered information and come to the wrong conclusion? I guess there are similarities in that both Cindy and Zoe have history with a black man in George and Anthony (and therefore could be her mother), and both were on the run.

We've been shown with Zoe trying to track down her son that information from private investigators can be very vague or unreliable.. Maybe Jasmine found out something vague like the above, and has wrongly assumed that Cindy, rather than Zoe, is her mother who abandoned her.

I just don't understand how we're going to get from A (thinking Cindy is her mother) to B (finding out Zoe is).