From a big perspective, foreign exchange is also an asset, so the supply and demand of foreign exchange plays a decisive role in exchange rate fluctuations. Although China has restrictions on the fluctuation range of exchange rate, the fluctuation of exchange rate is determined by the market supply and demand of RMB in the fluctuation range. Of course, if the exchange rate deviates from the will of the authorities, there is still the risk of intervention.
As for the manipulation you mentioned, it is basically negligible, and it is very difficult to manipulate the foreign exchange market.