There are two burdens from debt financing of the state. The primary burden is born by the present generation. Bondholders give up command over resources by lending to the state and society in general suffers lower standards of living than it could have enjoyed when the state directs the use of resources instead of entrepreneurs. The latter is the burden born by society at large.
The secondary burden from debt financing is independent of the primary burden. It occurs only if the state taxes some people in the future to pay bondholders. If so, taxpayers bear a burden and bondholders receive a benefit. Control of resources are not transferred to state and so, there is no burden on society at large.
In your case, then, the primary burden is suffered by the Chinese holders of U.S. bonds and by people around the world whose standard of living is lowered by having resources used inefficiently by the U.S. state instead of efficiently by U.S. entrepreneurs. The secondary burden occurs if and when the U.S. state taxes Americans and uses the tax revenue to pay Chinese bondholders. But this is not a burden on society at large.
It doesn’t matter whether or not the taxpayers and bondholders are in the same political boundary. The secondary burden will be suffered by taxpayers and offset by the benefit to the bondholders. So it’s misleading to say that future generations bear either the primary or secondary burdens. The secondary burden is born by the taxpayers (not Americans in general), wherever they reside, and offset by the benefit to the bondholders (not the Chinese in general), wherever they reside.