As far as I understand the definition of a second, the Cs-133 atom has two hyperfine ground states (which I don't really understand what they are but it's not really important), with a specific energy difference between them. Whenever the atom transitions from the higher-energy to the lower energy state, the difference in energy is released as a photon. A photon with that energy is equivalent to EM radiation of a specific frequency. A second is then defined as 9192631770 divided by this frequency.
In many places I see people claiming that the Cesium atom oscillates between the two states, transitioning from one to the next 9192631770 times per second, and that this is what the definition is based on. This makes no sense to me, and seems incompatible with the interpretation above - which is based on the energy of a single transition, not to rapid transitions. So I usually just dismiss it and/or correct the person claiming this.
When I saw the "oscillations" interpretation repeated in a video by the hugely popular Vsauce, I started to think maybe I got it all wrong. Maybe the second is defined by oscillations after all? Or maybe the two interpretations are somehow equivalent?
So, is there any truth to Vsauce's description? And if not, why is the misconception of oscillations so popular?