Is there any truth to interpreting definition of a second as corresponding to oscillations?
The definition for the cesium clock is:
9192631770 cycles per second is frequency of the radio waves which cause maximum resonance, a physically measurable condition, in the cesium atoms.
This corresponds to a particular tuning of the radio. Keeping it tuned provides the reference frequency cited.
You're correct and the video is mistaken. In fact, if cesium atoms were constantly oscillating between the two hyperfine states, cesium beam clocks wouldn't work at all!
In its simplest form, a cesium beam clock uses a magnet to separate a stream of atoms into two streams based on their hyperfine state; one state is selected to continue down the tube to be exposed to an oscillating magnetic field in the microwave range, and the others are wasted. After the microwave chamber, the stream is magnetically separated again, with one state (differing from the state that was selected the first time by a certain energy) hitting a target that responds to cesium atoms by producing an electrical signal.
The effect is something like the crossed polarizers of an LCD display. Since one state is selected before the microwave chamber, and a different state is selected afterwards, there is no signal unless atoms changed state in between. "Ordinarily", this doesn't happen, but if the microwave tube is bombarding the atoms with energy that corresponds to the desired hyperfine transition, then some of the atoms will absorb energy, make the transition, and be detected at the far end. By incorporating the beam and detector into the control loop of a variable oscillator, the microwave frequency can be maintained at the frequency that causes the hyperfine transition, independent of outside conditions.
The part of this that's crucial to your question is the statement that the cesium atoms don't change state between the A and B selectors unless something causes them to. If they were changing states at >9GHz, then small variations in the travel times for the atoms (which move at hundreds or thousands of m/s, but nowhere near the speed of light) would result in a completely random signal at the detector. Instead, we get a coherent signal because the rate of spontaneous hyperfine transitions is small compared to the time the atoms spend in the tube. Any type of interaction that can scramble the hyperfine state of an atom reduces the sensitivity of the clock, and eliminating these interactions is a big part of maximizing accuracy.
Yes, they really are oscillating between two different states (not simply driven in one direction), but as you suspect they are not oscillating at the reference frequency.
Rather than "just" sending radiation at the atoms to absorb, they also interact with an oscillating magnetic field (which is at the reference frequency). This field spurs some of the atoms to absorb or emit radiation. So both states are driven to the other state by the conditions inside.
A rather technical description of a cesium clock can be found at leapsecond.com
Some of the relevant items from it:
An applied radiation field of frequency appropriate to the transition. under discussion induces atoms in the F = 4 state to emit a quantum of energy, and those in the F = 3 state to absorb a quantum of energy; they are reversed in their magnetic moments following such transition, and are said to have flopped.
[...]
The magnetic component of the injected microwave field interacts with the atoms. If the frequency is at the transition frequency, 9,192,631,774.3133 Hz then atoms flop to the other transition energy state. Since their effective magnetic moment is 1hereby reversed in its direction, a second state selector magnet, the "B" magnet, can selectively deflect flopped atoms to the detector.