This page from the INZ regulations
https://www.immigration.govt.nz/opsmanual/#30897.htm is specifically talking about applying for residence for a dependent child separately, but the same kind of evidence is what will be required in order to include your step-children on an application for residence under SMC.
What most people with an NZ job offer do is to get apply for a temporary work visa at the same time as residence under SMC, as the temporary visa can be processed more quickly, and will enable the person to be in NZ already working while the residence visa takes its own time in the background. For the rest of the family to accompany the worker, the partner will need a partner-sponsored temporary work visa, and each child of school age a student visa dependent on the partner's visa, and these latter ones will need this evidence of rights and consent as well.