Excitingly means “in a way that makes people feel excited.” A story can end excitingly. A match can start excitingly. Though actually, speakers do not reach for this adverb as often as the tidy pair exciting / excitedly might make you hope. If the person is the one who feels the feeling, the word you want is excitedly: she spoke excitedly. If the thing is causing the feeling, people often just use the adjective: it was exciting; what an exciting end. There is a second, rather shiny use at the front of a sentence, much loved by news and blogs: “Excitingly, we found tickets.” That is the writer waving a flag — treat this next fact as a thrill. It is not wrong, but it is a little loud. Quiet everyday English is happier with “good news —” or “the exciting thing is…”.