Here's something I've wondered - and dismissed - but I'll ask anyway.
Is it possible that Jeremy did tell Julie all that stuff, but he was making it up? After all, if he'd talked about killing his family all that time, and then Sheila beat him to it, maybe he wanted Julie to think that he'd arranged it - sort of showing off.
I dismissed the idea eventually because I think he would have told her in the end that he hadn't really done it. Perhaps he did tell her that, but she didn't mention that.