In my experience, learning a second language to a high level involves some amount of disassociation. Only people I know without this experience spoke both languages from a very early age usually at home. So this tracks.
But there can be other factors as well. For example in social contexts can change sharply between languages. The way I talk with my family is very different from the way I speak professionally—at home I'm the youngest and at work I'm the boss.
I think your second paragraph is it. I myself and people I know learned different languages from the begging, from different persons. E.g. Portuguese from the great mother, Spanish from mother. Those are completely different relations, and they express themselves in the learned language.
But there can be other factors as well. For example in social contexts can change sharply between languages. The way I talk with my family is very different from the way I speak professionally—at home I'm the youngest and at work I'm the boss.