Sounds like you are describing the angry budgie sound..... the noise they make when they are pissed or want you to go away. If they are frequently making that noise then you should consider changing the way you are interacting with them, perhaps? If they are making the noise towards themselves however, well, make sure they don't tear each other apart! Otherwise, you can leave them be.
I thought it was a mad sound as well. They don't make it often and it doesn't last more than a few seconds. It isn't when I am interacting with them they do it amongst themselves. They all chime in for a couple seconds then they are back to their singing noises. I have never seen them doing it and getting violent just sounds like one calls out a warning then they all respond and then go about their business. It sounds just like the second video you posted!