Basically, for anyone who only speaks English: JYP decided that Tzuyu (age 16) needed to release an apology because it enraged the Chinese government, citizens, and some of their China business sponsors that Tzuyu held the flag of Taiwan. They assumed she insinuated that she's not Chinese because she chose to hold the Republic of Korea flag and Taiwan flag.
None of this is her fault because she is young and the photo in question has the other girls holding their homeland's flags, as well. It's crazy how they expect a very young girl (born in 1999) like her to have a political agenda.
She's caught in the crossfires of political ideological war, and now she's a tool for either stirring controversy, or maintaining peace after a little hiccup.