John,
I'll take a stab at this one. Hopefully it will boost my confidence if I am right. But I caution you to not take my explanation as correct until we have received the blessings of Luis, Jim, Benbo, etc.
For NCEES 138, look at the equation you're setting up:
V1=115kV
V2=24kV
V1/V2 = N1/N2 ==> V1*N2 = V2*N1
So, since the line and phase voltage is the same for delta, the V1*N2 term requires no sqrt3 and we'll do phase calcs instead of line calcs.
And, since V2 is wye, there will be a sqrt3 needed in the V2*N1 term to make sure it jives with the phase calcs on the V1*N2 term.
Phew, I know thats wordy. Hope I didn't confuse you.
Now, for NCEES 518, once again look at the equation you're setting up:
Vg=13.2kV
Vl=132kV
Il=75.93A
Vg/Vl = Il/Ig ==> Vg*Ig = Vl*Nl
So, it doesn't matter what's wye or delta configured because the V*I terms are corresponding to the same configurations when we cross multiplies the turns ratio. Hence, no sqrt3 needed.