Ms Alvarez, 55, and her family spent six months in Auckland nervously awaiting the decision, receiving financial support from relatives in Australia.
Soon after finding out their application had been accepted, the family moved to Rotorua.
Even now, separated by thousands of miles of ocean, Ms Alvarez worries her family is still at risk - a threat she won't go in to because of security concerns.
She was reluctant to give her opinion on political matters, but agreed the Government should help people in danger.
"If it is a life-threatening situation like my family, then New Zealand should help," she said.
Ms Alvarez now works at Cantabria Rest Home as housekeeper, but said she was trained in four different roles there.
She strongly denied the suggestion that refugees were coming to New Zealand looking for hand-outs.
"We haven't asked for any help. We're not adapted to asking for help, because in our country there is no support."
Although there had been some instances of abuse - "people telling me, 'go back your country'" - Ms Alvarez said, on the whole she had felt welcome in New Zealand.
"It has been a very big experience because of the different culture and the different weather. The people are very friendly, and some are very supportive."
It hadn't been easy adjusting to a new country; Ms Alvarez said it had taken her a year to feel confident speaking English.
But now, four years after her arrival, Ms Alvarez speaks passionately about her desire to keep learning.
"We are attending computer classes. Maybe if I'm lucky I will one day get a job in computing - or at least for my son ... My thinking is, it's never too late to learn."