That's also explained through the animus. The event already happened, so the death cutscene is how it "happened" in history and tells you the story, but the rest of the run up is part of the animus simulation that you went through to get there. So the animations breaks down and pauses for that important story bit, and is recreated when the story bit is over to prevent bugs.
I'm not sure if they actually say it in the main story or you have to find it through the animus information but it is there somewhere.