Thanks for the answer.
Now I understand. I understand protecting the country as well. But now what option do I have? Should my family apply for a visa via London and ask for connect their application with mine? What should we give as a reason in cover letter? What do you think about this situation? Can this incident influence on their application? What do you think? In what way should we explain this situation?
The best thing is that the advice for my family to arrive and apply being in NZ I was given by one of the official immigration advisor.