You said (AND I QUOTE! lol)the question was, where do you live? You said in several states COMMA one (as in one of the states) in Australia and ONE in New Zealand.
So. no.
If he had meant to list the states, the proper punctuation mark would have been a colon. Since there was no colon, we can rule out that he was referring to places in Australia and New Zealand as states. Also, even though commas are not required before the word "and" in a list, he did place one between Australia and New Zealand, which signifies that those are not part of a list of two places, because if it had been a list of two places, there would be no comma.
I will rephrase his statement to make more sense to you.
"I live in several states around the US. I also live in Australia and New Zealand."