1) Use China Census data at Country level to derive total population count per county.
2) Create a land area grid such that each pixel has the value of the square km's it represents. (This land area grid masks out inland water at the sub-pixel level). This means that not all of the pixels in a given county will have the same land area, because some of them might contain water bodies which would subtract from the total area of the pixel.
3) Add up the total land area per county and determine the total county Population Density.
4) Distribute the population count on a per pixel basis by multiplying the Pop Density of the entire county by the land area of each individual pixel.
It is not unexpected, and in fact is quite regular to have variation is the values of pixels within a given county. This is due to the fact that each pixel has its own land area.