Well, we presume it does, and we act (and can't hardly help but act) on that presumption, and so that seems like a good enough answer from one side. I hold to that one.
But I also am fascinated by the playing around with time performed in literary philosophy by authors like Borges and W.G. Sebald. And the question of where the border is also difficult to figure... So to the extent that I am convinced or at least held suspended and enthralled by the way some play with the question, I believe it remains good-humoredly open.