The difficulty is that Unicode itself does not distinguish Chinese from Japanese from Korean. It considers the character sets that they use to be identical, just as it considers Latin uncial (used in writing Gaelic), Latin blackletter (formerly used in writing German), and modern Latin characters generally used to be identical.
Unicode calls this unified script the Han script or the “CJK” script. See http://www.unicode.org/versions/Unicode5.2.0/ch12.pdf for a discussion of the rational behind not considering Chinese, Japanese, and Korean characters sufficiently different to be encoded separately.
Similarly Arabic characters are unified with one another, although different styles are used in different countries, and different styles of runic characters are unified with one another.
To select the proper Latin letters or Arabic letters or Han-characters you must individually select fonts that display the characters properly for each language you wish to see.
If you have set up your computer to display Korean by default, then both Japanese and Chinese text will also appear using the Korean forms of the letters. You must individually change the font in any editor for any Japanese and Chinese text to a font that is intended for Japanese or Chinese.
Word processor files specify which fonts to use, but if you do not happen to have the same fonts that are specified, the word processor may pick up another font that is in an incorrect style, perhaps attempting to display Chinese in Korean forms of the characters or Korean in Japanese forms of the characters. You can fix this by finding and downloading the missing fonts. See http://www.alanwood.net/unicode/fonts-east-asian.html for East Asian fonts which are either free or very low cost or come with operating systems. You can also specify in most word processors a list of font substitutions in which you tell which font you wish the system to use in place of any specified font.
Word processors also usually allow you to set the default language for documents (and runs of text within a document). Simply resetting the default language in a document from Korean to Japanese may change the default font from a Korean to a Japanese font.
Most web browsers allow you to set different default fonts for Chinese, Japanese, and Korean text and the browser will attempt to figure out what language the text is in, or will use HTML language tagging. This will not always work correctly, especially if the text you are attempting to view specifies particular fonts.
In short, your computer appears to be working as well as should be expected.
Just remember that Unicode considers that Chinese, Japanese, and Korean all use the same script, the Han script or CJK script, but that the different languages use different styles of the script. When one of these languages comes out displaying the script in an inappropriate style, you must change the font to one in the appropriate style.