The ship has many things it has to do before it reports the overboard - like make sure it really happened.
I assume there was something about the video that didn't make what happened clear or else they would have reported it sooner.
I read that they assembled all the passengers and took a roll call first (on Allure? 6000 passengers!)
I am the editor, but I also speculate, ask questions and play devil's advocate. I reserve the right to change my mind.