Just my opinion BUT I think Jeremy told Julie that he had hired a hitman because he knew the story wouldn't check out and he could simply say she was lying because they had fallen out. He couldn't tell her too much just in case she told police - which in the end she did.
While it is possible he said it in case she ratted him out, more likely it was just because he didn't want her to think he was so coldblooded that he killed the kids. She made a big deal over how oculd he do that. He didn't want her to be scared of her.
If he were truly thinking in his mind maybe she will rat me out and calculating then th ehitman claim is to discourage her from ratting him out because she will be in fear of the hitman coming after her as opposed to just having to fear him.
I personally think Jeremy was just saying it so she would not think he was as cold blooded as he was not thinking about trying to discourage her from ratting him out or in case she did for the story to flop.
It could be a mixture of these things though there is no way for us to know for sure what was running through his mind.