Steve and I feel that since we want to go to NZ and call it home, we will make every effort to become Kiwi. Not to say we won't have pride in where we came from or what we've accomplished. I think one of the biggest reasons we have this mentality is because of the problems SoCal faces every day with illegal (and legal) immigration, and the aggressive attitudes towards Americans the immigrants show. When I patronize a business in the States, I don't want to be treated poorly just because I'm American.
If one comes to a country with the intention of gaining something for oneself and one's family, one should respect the country's culture and people. (even if in your heart you still consider yourself your first nationality)
BTW, this is just my opinion, and not a criticism of ANYONE! Everyone is entitled to their own thoughts.
As to when to consider yourself a Kiwi, I'd say it's when you decide you are; it can happen at any time during the process!