Judging by the line "as if he could see the future" the contractor doesn't know about Mirai's foresight.
The gunman's doll looks like Meguru soo possibly a yandere situation or, as someone commented on an earlier chapter, some sort of inheritance dispute.
Honestly, if it's either of the two above, it's a little disappointing. To me that dumbs down the whole 'time travel' to a cheat skill rather than a fully fledged mystery. Then again, maybe the conversation with the mom will reveal more.