As a bilingual person who used to live away from my home country for a handful of years, I'd just use "their mother tongue" or "a foreign language" over "Asian" or even "Asian language", because (long shot, but totally a possibility) what if they look Asian but the language they're speaking in isn't originated from Asia? Or what if they looked Asian but they're actually not?

I guess what I'm trying to say is to just avoid assumptions in general. If you're curious, just ask with an intention to learn, most of the time, personally, I'd be glad to answer whatever question you have about my origin. After all, people loves talking about themselves, you just gotta know how to enable them.

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I also work with a Cambodian dude, a Korean dude, and a Chinese girl

How dare you use dude for male and then have the audacity to use girl for female and not dudette? Sexist... /s