Like I said...all you need to do is vector additions.
For example, say you have delta connection in the primary and your voltages are
VAB=1<0
VBC=1<-120
VCA=1<-240
And you do a wye connection on the secondary and connected
the secondary winding of VCA between a and neutral, that is Van = VCA
the secondary winding of VAB between b and neutral, that is Vbn = VAB
the secondary winding of VBC between c and neutral, that is Vcn = VBC
Now, you turn around and want to measure the line-to-line voltages on the secondary side...what are they?
Vab = Van + Vnb = Van - Vbn = 1.732<150
Vbc = Vbn + Vnc = Vbn - Vcn = 1.732<30
Vca = Vcn + Vna = Vcn - Van = 1.732<-90
So, not only is there a phase shift, but there is a ratio in magnitude for transformers with 1:1 turns...1.732 from delta to wye and 1/1.732 from wye to delta.