Exchange Rate Determination
1st of all, regading your remark


  ... , it is solely interest rate differential brought about by monetary
  policy that cause exchange rates to fluctuate...


That's just because it these models the internet case is isolated (like the joke of economists needed to change a light bulb)

As to your question, its always a combination between interests/ exchange rates and trade:

Per your example:
When China lowers rates, effectively increasing money supply, the Yuan decreases and make exports more profitable
Once exports occur, dollars come back to China, and converted to Yuans, making the Yuan increase back.
To keep exports more profitable to China, a constant increase of money, lower interests rates, are needed. This, in turn, can create local price surges. Essentially the local economy subsidizes exports

What China does though, is not exactly that,  even if similar
China holds its foreign exchange rates low, and its interest higher. That sounds a bit contradicting, but its possible, if China's government absorbs dollars.
So on one hand, Chinese exports are cheap, and on the other hand, the Yuan is a strong local currency. Furthermore, due to yhe e, export accelerated growth, wages and wealth has increased...