People may have told you that only indefinite nouns take the final -n sound, but that is incorrect. Many definite nouns take them as well. It's the definite article that prevents the final -n from sticking to the word, but if a word is definite because it is a proper noun for example, then many proper nouns do take nunation. Feminine proper nouns and most proper nouns of foreign origin don't, however.
When to use it is a complicated question about which you could fill a chapter of a book, but basically, noun cases are like the difference between "I" and "me," or "he" and "him," only applied to all the nouns. You say "kitaabun" ('a book') if you used the word "book" where you'd use "I" in a sentence, "kitaaban" where you would "me," and "kitaabin" where you would "my."
Why would nunation of a proper name sound any more strange than anything else in a completely new language that is foreign to us? Virtually everything in a new language family is new and different and therefore "strange".
It clearly says "Rawedun suurii". Maybe your mind is transferring the "a" sound in "Rawad" and you're "hearing" it in the wrong place. After listening to the sentence a few more times, I'm sure you'll hear it correctly.