The way the scene’s shot and the way Adam Driver and Daisy Ridley give their performances, it makes it clear that he’s just getting her to admit what she already knew was true. He may (may) be manipulating her, but he’s not manipulating the truth.
Either way, if he was manipulating her here, why not go with the Palpatine manipulation right off the bat? Pull the same stuff he says in TRoS instead of waiting a year? What happens when Rey finds out she’s not a nobody? Because that’s definitely going to eventually happen.
The ways of Palpatine are mysterious. He both wants to kill Rey and use Rey. This was also true of Luke in the OT.
Yes, Kylo makes Rey admit what she remembers about her parents. She did not know her parents had any connection to anything because they were on the run. JJ had some reason in mind why they didn’t come back for her. Trevorrow’s script did nothing to ever answer that question. JJ returned and found an answer that fit beautifully with both existing films. Palpatine had her parents killed because they were not willing to be used. And as long as Rey was opposing him, he wants her dead. But if she is willing, he can use her. He tells Kylo of her parentage and Kylo tells her. It was unknown before and Kylo uses that knowledge to mess with her yet again. He did it in TLJ with her being a nobody and he did it with her being a previously unknown Palpatine in TROS. The only change to the story of Rey’s past is that she remembered that her parents were running from something. This echoes back to Maz saying that Rey knew her parents were never coming back. When you look at the details of the stories, nothing in TROS conflicts or contradicts or rewrites anything in TLJ.