Factual error: In the episode where Kyle, Lori, and Josh first go to the pool together, Kyle jumps off the diving board, but he's only in the water for about three seconds before he sees Amanda, who is already swimming toward him. This means that he was in the water for just a second or two before she jumped in. That isn't enough time for anyone to appear to be drowning, especially to a trained lifeguard like Amanda.
Suggested correction: First, at least 10 seconds pass before Amanda jumps in, not 1-3 seconds. But that doesn't mean only 10 seconds passed in the show. But additionally, Amanda already knows Kyle has memory loss and could be thinking Kyle forgot how to swim or forgot that he can't swim. So she goes to get him.