I’d always just assumed that was Snoke lying through his crooked yellow teeth to further manipulate Kylo, as Sith(-adjacent) lords are wont to do. He’d seen into Kylo’s mind and discovered their bond, deciding to take credit for it to try and undermine/complicated their feelings for each other.
I have no doubt that is most likely going to be the canon answer at some point (or already), and was the intention the writers of TROS had when creating the concept of the dyad. But it’s just kinda messy. And they didn’t have the opportunity (like us) to go back and change certain small details in the previous films.