What do you call a speaker who does not follow a standard pronunciation?
Solution 1:
Such as person speaks with an accent (or has an accent). You could describe the situation further to be specific. Obviously, all speakers speak with their own accents, but the phrasing above implies that the accent is not that of a widespread dialect.
In your scenario, it is unlikely the person would speak with an accent. Usually people who learn a language at a young age and achieve native proficiency in it speak with no accent. (Where "no accent" means with an accent reflecting the dialect(s) they grew up speaking.)