My guess is that what they're doing is relying on very subtle differences in timing and pitch to zero in on which overtones belong to which notes. I'll bet that if you had an instrument which was tuned and intonated mathematically perfectly, and if you hit the start of each note in the chord precisely at the same time, then you might actually confuse their engine.

Still, with most instruments, the start of each note is mostly noise, so I don't really know how they're solving that one. Perhaps they're not. Maybe the noise just doesn't get moved along with the rest of the note. Not important for frequency domain alteration, but possibly critical for time domain alteration.