There was a question I'd had, the shot Kincaid took wasn't any past event written down or even discussed...
If a phone call travels over
any portion of digitized network -- and that's almost inevitable, these days -- then it's "written" within the remit of the Archive. So Ivy had a copy of the phone-call.
Ivy is a teenager at this point, so of course she was eavesdropping on her ‘parent’. Occam’s razor.
<heh>
A very "human" notion, I like it! Thumbing your nose at the whole galaxy of spookyside wierdness-explanations.
But Jim has already confirmed that the Archive contains digital info, the entire Internet.
So, digitized phone lines, too.
Even so, it doesn't explain why she didn't insist that he didn't shoot Harry at all.
Having accepted the contract, Kincaid would never relent. Ivy
cannot "insist."
Unless she is willing to permanently imprison him, engage in memory-erasing magic, or otherwise "remove him from play," Ivy can't stop the hit.