The filter topology and number of poles (which determines the filter slope) determine it's phase behavior; digital/analog doesn't, in and of it self, have any correlation.
Or in other words: As long as digital equipment emulates analog circuitry (as it is the case with IIR filters, recognizable by using the same charateristics as analogue crossovers, like Linkwitz Riley, Butterworth, Bessel etc.) it will cause the same phase shifts, group delays and so on.
There are digital filters called FIR filters which can separately process frequency response and phase. These filters can't be done in the analogue domain.
