Hi McFly,If I were to guess I'd say ADC to DSP with FIR and IIR filtering to DACs to amps out. The in app option 'phase correction' can be turned off to bypass the FIR filtering (but still keeping the IIR filtering and nice frequency response) and allows for less latency and less video/audio lip sync issues.
You're absolutely correct about the signal flow and the phase correction. With the phase correction disabled, the latency will reduce and the magnitude response will stay the same. The FIR filters have been designed to have an all-pass behaviour, altering only the phase response.