They're not worried about CSAM. They worried about TikTok users being influenced during an election campaign.
And yes, it is a moderation issue. Specifically, the US doesn't want the current moderation team to be in charge of moderation.
Disclosure: I don’t use Facebook, Intagram, Twitter, nor TikTok
To put it in perspective, about a quarter of the US population uses TikTok. And politics are a major discussion point with the political content you're exposed to selected by an algorithm that is opaque and constantly changing.
It absolutely can be used to change the result of an election. And China has meddled in elections in the past (not least of all their own elections... but also foreign ones:
"China has been interfering with every single presidential election in Taiwan since 1996, either through military exercises, economic coercion, or cognitive warfare, including disinformation or the spread of conspiracies"