Combustion instabilities (oscillatory combustion) in rocket engines are caused by coupling between the combustion processes and pressure oscillations. Frequencies can vary from 100-20,000 Hz and pressure amplitudes from 10-1000% of the engine’s steady state pressure. Combustion instabilities can produce destructive vibration up to RUD.
Acoustic resonators are commonly installed in combustors to provide passive acoustic damping of high frequency combustion instabilities.
Also, injectors can be tuned to act as half-wave resonators and provide acoustic damping. This is particularly effective for managing intermediate frequency oscillations to prevent them from becoming high frequency oscillations.
I’m venturing out of my pay grade, but I assume that measuring and tuning the dominant acoustic frequency of an engine would be a part of test firing. Other factors being equal, I would assume the lowest energy oscillations would be tuned in (lowest frequency, lowest pressure amplitude)
When multiple engines are mechanically bolted together, interactions of these frequencies would need to be taken into account. Similar, but slightly different, frequencies could produce beat frequencies very different from the primary frequencies. This could produce unexpected structural loads or interact with other vibration modes such as pogo vibration
Addendum. I'm going to delete my answer. The quote in the OP makes no sense to me and my answer doesn't clear anything up. The vibration problem on Apollo 6 was attributed to pogo, not combustion instability. Hopefully other information will come to light on what "pulling the booster off balance" is all about.