RSAF has used SIA in the past, but they also use TG for ferrying troops to Thailand, BI for Brunei and Eva Air for Taiwan.
I guess up till a year ago, SIA didn't have spare 744s for lease and Air NZ did. I still don't see how Air NZ can do it cheaper than SQ by ferrying a 744 empty to SIN, ferrying the troops to ROK and back then ferrying the 744 empty to AKL.