I've been wondering about that too for a while now. That's probably one of the flaw of this manhwa. But, maybe this is the setting so that it won't be hard for the author and translator and readers to switch languages and it will be easier for characters to do the conversation smoothly.
I’m guessing when they’re in South Korea, everyone speaks Korean, even those that come from a different country. Usually when people go visit another country they either speak/know the language or have a translator. I guess with the world awaken academy they speak the most common language, which is English. This is just my guess. We as readers know what is being said.
I dont get it, How come they understand each other when they literally in different countries. At first, I thought Kaiden lives in S. Korea too cause he can converse with Jiwoo perfectly fine. Same with those foreighn students. Does language barrier imvisible in this manuah? (⊙…⊙ ) Nevertheless still my number 1 manuah that I reread from time to timeヾ(❀╹◡╹)ﾉ~