Unfortunately CJK support requires a few factors that themes must comply with.
For starters when you change the font in theme settings menu, it only changes the theme's "default" font which is a single font used for menus. Third party theme creators can choose to use the default font for other parts of their theme, which would then change if a user changes the font setting.
Some themes though use multiple fonts instead, which are hardcoded into the theme and cannot be changed by settings unfortunately. In cases like this, themes must support CJK fonts themselves.
FreshOS, Infomatrix, Adwaitapod and Themify are the only themes I can think of right now that explicitly support CJK characters. Hopefully this helps