IF YOU DIE IN THE MATRIX YOU- no wait, that doesn't quite fit here. Anyway, with them revealing the "twist" so early I get the feeling there's still more to come.
More importantly, how do you define flow of time and the present "now" in a data storage where everything exists in the same instant? Does time only exist when someone logs in to review the record? And how does it generate responses that are not on record, that is to say when someone tries to interact with it? They did not say there was anything simulating the people or the world, only that it was a record. Further, what happens when you bring part of the record (a person or an item or whatever) across the edge of the recorded area.
Actually, a more credible explanation is that mister ten-years-from-the-future is altering the recording (does he have the admin privileges for that? Or permission?) to make it look like it is responding to his presence. He cannot act like a god and change everything because he needs it to be the "young him" that saves the girl, so he chooses to alter the record in "real time" instead. So he is playing out a wish-fulfillment time travel story for himself in front of the computer console.
Which is still a better explanation than people simulated by AI for no good reason.
Well, unless the company that does the record is in fact selling some sort of full immersion VR experience to thousands and thousands of people. Perhaps with each subscriber getting their own little instanced version of that past, as the last thing you'd want is an MMO experience. It is noteworthy though that he says at the beginning that he "finally did it" which might imply illegal access. Have fun getting all your change commits reversed with a single rollback command...