For a country like China, the exchange rate between US dollar and RMB is very important. China has been trying to solve the problem of capital flight for many years, and the appreciation of the US dollar will make the problem even more difficult. Although China has huge foreign exchange reserves, they do not want to see the ongoing infrastructure investment and growth expectations negatively affected by the appreciation of the US dollar. A stronger dollar will enable China to use its foreign exchange reserves to rescue the market and prevent the RMB from further depreciation.
So, since there may be potential downside risks on a global scale, why should the Fed do so? The dual purpose of the Federal Reserve is:
1) Maximize the employment rate.
2) Keep the price in the American market stable.
Of course, they also took into account the global economy while changing their policies, but their main task was to save the American economy from the "hot water".