That's a good assumption, And I won't try to deny it. If that were the case, then his powers would be no different from mangas like: All You Need is Kill or Re:Zero. But I don't really know, I feel like the pond is a well deserved flaw to his powers. Plus all the covers suggested that it's the lake. But who really know? ╮( ̄▽ ̄)╭
if he gets to old age or get a terminal disease he will have to relive his last day over and over again with his brain damage getting worse and worse till i imagine he would end up a vegetable, and if his ability is automatic not conscious then every time they unplug him the day would repeat again, unknown to anyone else the day would repeat infinitely. you know what would suck, if someone else had a similar temporal power that had to live the same day over and over again not knowing why the day repeated. like groundhog day.
if my assumption is right, his ability has nothing to do with the lake, he has to just die, i bet he will hit the ground and wake up to repeat the day again.