You are quite right about that, but if Obama had taken some positive action to confirm that new citizenship after attaining his majority, such as applying for a passport, then a taint might have fallen over his citizenship. Given State Department rulings and actions in similar cases, Obama probably had nothing to worry about. But, this was a political issue and not a legal issue, and still is in my opinion.
I'm unclear why there would be a question of a "new citizenship" - not trying to be difficult, just to understand what "new" means in this context?