Memory is fuzzy but I went through this last fall.
You got the right alternator for the kit but it won't work with that (GMPP) ECM as that alternator needs a PWM signal in order to regulate voltage.
GMPP solution of leave it unplugged and it will run at 13v was not acceptable to me.
We used a AC Delco 25766345 alternator for a 05-07 CTSV and wired that to the ecm and it charges at 14.6v It has the same connector as your current alternator but only 2 pins in the middle.
More info here.
https://ls1tech.com/forums/conversio...or-wiring.html