The captain acted decisively and communicated clearly. I teach firefighters and paramedics how to communicate on the radio. You always want an inverse relationship between the stress level of the situation and the intensity level of your radio transmission. Speaking 20% slower and being understood is much better than speaking 20% faster and constantly repeating yourself.

Talking to ATC is far down on your priority list in emergencies. First priorities are to fly the airplane, figure out what's wrong, decide on a course of action and head in the right direction.

Only after all those things are done, should you take time to talk to the controllers. In these situations, you do what's necessary and then, when convenient, you advise the controllers of the actions you are taking.

What would urgency sound like, speaking really loudly and quickly? If so, how would that be better than her measured cadence making sure she and the tower are on the same page?