Well, considering Temmie Chang and Toby Fox made the game, and they both have inserted themselves as dogs, I assume that Tem and Annoying Dog have secret god-like powers and can remember resets.
I think that the "feeling of being watched" temmie from the village is always in the walls, and goes back to the one at the tem shop through the hole in the wall.
Theory: Temmie knows about time reset and remembers resetted timelines because she knows when frisk dies and she lowers the price for the temmie armor.
This also mean that temmie has spies everywhere that know abt time reset OR that everywhere frisk goes Temmie is always somewhere stalking him
Caption this Meme