The action of the mask dropping does not start the flow of oxygen. The PAX must pull down on the mask to remove the pin, that action starts the chemical reaction. The mask will not inflate initially.
It sounds like some cabin crew are not well trained and had no idea of what was happening. The "get down" command sound like a brace for impact command?
At my airline the Captain will make an announcement once established in the descent.
It's easy to Monday morning quarterback and we have to remember emergencies are never neat and tidy, even in training when you know it's coming.