Y'know, I don't know where we got sentient time from for this story. It's just the way time travel works. We can't go faster than the speed of light, but no one today talks about how Light just "knows" when you're about to go too fast and smacks you around. It's merely a consequence of the physical laws and the universal constants. No one in the story gave any indication that they believed there was some sort of entity behind the limit on repeat visits; it's just how the stuff works, and running into your time duplicate is akin to running into a brick wall in a racecar. (The "visible signs" thing was presumably a nod to the idea that observation collapses the quantum waveform, albeit one rooted in a common misconception about what constitutes "observation.")
Anyway, off to cull some comments. I just didn't see anyone address this initial complaint beyond amusement at the idea of sentient time. (Shades of Astro City and "The Nearness of You," perhaps?)