US does not
If you think they should then China should also have jurisdiction over American citizens, which in this case would mean American citizens must comply with Chinese laws when it comes to ByteDance.
Generally speaking, I am of the belief that a country's jurisdiction should end where its borders end.
However, in practice things get a little more complicated:
For example, the US government tends to believe that they are right to prosecute anyone anywhere in the world if their alleged crime in some way, shape or form entailed a financial transaction executed in United States Dollars.
So for example: generally speaking, the US won't prosecute non-US citizens for buying Russian hydrocarbons with Russian currency, but they will or at least may prosecute you if you buy Russian hydrocarbons with American currency.
Is that reasonable of the US?
Moreover, the US, will at times, also prosecute foreigners who commit acts of violence (e.g. murder) against American citizens on foreign soil
This is probably too much for non-Americans to consider acceptable, and is arguably a violation of foreign sovereignty.
Yet, China has also prosecuted and even executed foreigners responsible for the murder of Chinese citizens abroad. The most well known case involved foreign nationals who murdered 13 Chinese sailors on the Mekong River in either Thailand or Burma around 2011.
Though these days, even those engaging in telecom fraud against victims located in China may find themselves extradited to China.
Is this reasonable of the US and China?
More than half of Americans are on TikTok and are on it for hours each day, do you think they'll stop doing that just because they have to visit a website to update their app? Apple is additionally subject to retaliation from China for doing anything outside US.
But even that point is moot, you don't need the app to view TikTok, they can and probably will just ban all American users from posting for their own safety. US government gave China an excuse to ban all American influencers, might as well use it.
I agree that there are certainly ulterior motives to Congress' decision to force upon TikTok a ban-or-sale, but that's the case with a lot of, if not most legislation. Such is politics . . .
Though at the end of the day, fairly certain that the US authorities can ban Americans from accessing TikTok with ease.
All they'll need to do is to seize TikTok's servers physically located in the US. No infrastructure, no service.