The right way to solve your problem is to go to Firefox Settings/Language and Apperance/Fonts, then click on "Advanced".

There you can set what fonts should be used by Firefox to display each script/language, including Chinese, Japanese and other CJK variants.

If you do not configure this, then it is indeed unpredictable which fonts will be used by Firefox to render the Web pages, unless it can match exactly a font requested by the page.