How to treat dual affiliation in a journal article
Where did you do the work that the publication is based on? You need to check the affiliation requirements of the publisher, as well as your contractual obligations with the Chinese institution. Maybe write to the journal editor and explain your situation. Most journals state something like "Present the authors' affiliation addresses (where the actual work was done)..." and "If an author has moved since the work described in the article was done, or was visiting at the time, a 'Present address' (or 'Permanent address') may be indicated as a footnote to that author's name. The address at which the author actually did the work must be retained as the main, affiliation address." (emphasis added, from Elsevier archaeology journals, e.g. https://www.elsevier.com/journals/journal-of-archaeological-science/0305-4403/guide-for-authors) and "The primary affiliation for each author should be the institution where the majority of their work was done. If an author has subsequently moved, the current address may also be stated." from Nature Publishing Group (emphasis added). The Chinese institution, which wants to be acknowledged for supporting you, is not legally the primary institutional affiliation for work done in a US institution. You should be wary of misrepresentation, which could violate publishing ethics.