You wave for a bit, until Skittles (the one you were waving at) disappears to go do the stuff in the frog temple. Perplexed, you move on. However, an explanation is in order. Skittles, the one that just left, saw you and his FUTURE self in his perceived present. Then, later, when you were trying to get out of the temple, he took you and himself into the past, so that PAST Skittles could see his FUTURE-now present self. Thus, giving him the idea to time travel all over again in an infinite time loop. It's not quite self-starting, as Skittles had some knowledge prior of being able to time travel (the secret lab), and he has knowledge afterwards, so there's no juju nonsense.