As you’ve surmised, the KICKR doesn’t measure cadence directly. Instead, it analyzes the pattern of your power over time. It assumes that power will be lowest when the pedals are in the 12 o’clock/6 o’clock positions. By measuring the time between low points, it can estimate your cadence.
One implication of that approach is that if you turn the pedals but are spun out (I.e. not applying any force to the cassette through the chain), the KICKR will measure zero cadence. Likewise, if your pedal stroke becomes highly uneven (which sometimes happens during cadence drills), it will not be able to measure cadence accurately.
Hope that helps.