It would have to be after the war, since the Yeerks would easily find them once they knew Visser One's host's son was an Animorph. Even if they changed everyone's names, though apparently the guy's real name was Jake. One of the Animorphs has a parent that runs The Gardens, and frankly I'm surprised she wasn't taken since the battle morphs are mostly from The Gardens. Jake, Marco, and Cassie would be taken pretty quickly. Every controller would grab their brother, every administrator at the Gardens who had a daughter would be taken, and Visser One would be getting a call asking about her host's family.
I can imagine there being more than a few people in California with Rachel's mother's occupation, and Tobias isn't Human anymore. The Yeerks can be stupid sometimes, but even this wouldn't fly.