How do you explain a new authority figure who isn't mom or dad?
I always tell step-parents, or if a mom or dad has a significant other that's involved with the children, to always take the back seat when it comes to parenting the children. They're kind of the co-pilot to that primary parent's discipline of their children until the children get used to that person.
They should focus on being the proactive parent trying to prepare kids for situations and using effective praise, such as praising children for different situations. I would leave correction, at the beginning of that relationship, up to the primary parent and be the wing man on that versus correcting them.