Do electrons actually vibrate?
The electrons emit cyclotron radiation, because they are being accelerated by a magnetic field. The acceleration is always perpendicular to the electron's velocity vector, so they don't speed up, they just turn in a circle. However, all accelerating charges emit electromagnetic radiation, and in the case of an electron moving in a magnetic field in this fashion it is called "cyclotron radiation". In other contexts it is called "bremsstrahlung", and so on. Physicists often have multiple names for the same basic phenomenon manifesting itself in different circumstances.
Add "electrons vibrate" or "everything vibrates" to this account adds nothing and obscures the actual source of the radiation, which is continuity conditions on the electro-magnetic field. These conditions are described by Maxwell's Equations, which predict such radiation. There is exactly nothing in Maxwell's Equations that could be said to describe a "vibrating electron" in this context.
The summary is equivalent to an account of a baseball game written by someone who has never seen a ball, or a game, of any kind. It is depressing that "science journalism" scrapes along at a standard that is an order of magnitude below anything found in sports journalism, which is itself not exactly a paragon of insight and coherence.
The paper itself can be found here: http://arxiv.org/pdf/1408.5362...
It is a beautiful piece of work that really does open up new doors to precision measurement of beta spectra.