No reverberation unit is required to generate them after the fact, they already exist in the recording, which is why no quad decoder I’ve ever come across uses such a thing.
Of course substracting Left from right bring up the differences and reveal a lot of the recorded echoes and stereo effects.
Then you state the effects settings are nothing else than variations of the matrix equations to bring up more or less of these echoes effects.
The mystery of the little box is solved then.
It only contain some matrix circuits in a shielded enclosure.
i'm still puzzled by this diagram and the hard to read content of the first box