My guess is that she got sent very limited information, but that more and more puzzle pieces fall into place as she experiences more.
I think a in depth investigation on all her lines is needed honestly.
Her first few lines when she gives Cloud she shows obvious knowledge about Cloud, she also talks about giving the flower to his girlfriend, but I don't think this is an explicit reference to Tifa, although I think that when Cloud mentions her name, these might be pieces of her memory falling into place. Like she had a general memory of "Tifa, good, Cloud" or something, but didn't really place who Tifa was, or her role, until Cloud mentioned her, and she met her.
Aeriths first words on reuniting with Cloud in the church are obviously bullshit, she KNOWS he's a mercenary, and clearly knows he was her bodyguard in the OG. Now again, these could be some flashes of memory like "Cloud, mercenary...my bodyguard". But in this case, it feels even more like she's trying to directly recreate her meeting with Cloud in the OG. She seems a lot more sure of this.
I just get the distinct impression that only things that are clear in her mind are the things impacting HER destiny, the things that the whispers would actively try to make sure happen, the things that define her destiny.
She knows Cloud, she knows Sephiroth, she knows Jenova. But when it comes to things like Tifas identity, that's more of a shadow falling into place. Things like Zacks fate, that's her personal interest, it's not relevant to her task at hand, while the fact that Cloud is not himself, perhaps is.