Myriad Pro (or any of the earlier Myriad versions) has never supported any of the Far East languages. You will need to format text in those languages with a different font.
My gut feeling is that you are dealing with a composite font. These fonts take Latin glyphs from one font and CJK from another font, but present them to ID as a single font - and if you don't overtly name your composite font something that makes sense, the default name is usually pretty incomprehensible. Did your project start on an East Asian localization of ID?
It's funny that it's based on Myriad, though - the Latin glyphs from Myriad Pro and the Latin glyphs from Kozuka Gothic Pro differ in scale and weight, but are very similar to one another. So similar that I would have simply used Kozuka Gothic. The same is true of Adobe Heiti (but you only get one weight free with ID; maybe that's why your provider felt the need to make a composite font based off of Myriad).
I forgot to mention that I assume you are using an English-language-localized version of ID; East Asian versions of ID offer composite font tools. You may find World Tools Pro useful if you need to work with these fonts in English-language InDesign. On the other hand, maybe you're a Creative Cloud user - it may be easy for you to switch to Japanese ID for a project, I don't know for certain.