You use controversially when you tell people that what comes next causes a lot of argument, because many people care and they do not agree. “Controversially, the school banned phones.” It is a warning flag at the front of a sentence, much loved by news writers. It does not mean the speaker is shouting, and it does not mean the idea is wrong. It only means the subject is hot. The adjective is controversial; the noun is controversy; this is the adverb, the “in that arguing-about-it way.” Though actually, writers sometimes use it to protect themselves: they can report a decision and, with one word, show they know it will upset people. It can also sound a little theatrical if the disagreement is small. Save it for things people truly have strong feelings about.