Yes. Think of the average North American you know who grew up in a household with one immgrant parent and one local parent. In adulthood, how does the person compare with someone who went through the old country's education system? Again, the person may be illiterate in the relevant language.
How would removing extracurricular tuition affect the result? (Heritage language "buxibans" for kids are definitely a thing in NA, but not so much in Taiwan, unless the language is English, Japanese, etc.)
How would adjusting the immigrant parent's educational background to match that of the average foreign spouse in Taiwan affect the result?
If it's the language you grew up speaking with your mother, it's reasonable to call it your mother tongue. That doesn't mean learning it at school is a waste of time.