Unless the filter is of linear phase type (it will specifically say this or say FIR), then it is an analog mathmatical model even if it's implemented digitally.
-Passive uses inductors, capacitors and resistors in between the gain stage and the speakers so it will create a phase shift due to inductance or capacitance.
-Active uses capacitors and resistor components + opamp circuit as a buffer in between the source and the gain stage and allows you to have a variable type. It also creates the phase shift due to the capacitance.
-Digital IIR crossover is done via the math behind the passive OR the active model (linkwitz, butterworth, etc) and therefore it still has the phase shift occuring
-Digital FIR crossover is done via convolution and it creates linear/minimum phase crossovers so there is no phase shift at the crossover frequency.
For every 6db/octave there is a 90 degree phase shift at the crossover frequency.
6 = 90
12 = 180
18 = 270
24 = 360
So it should work the same in your case since it is nothing more than a basic active analog model.