The decision caused a backlash online, with an opinion piece written by Ms Jones in the Otago Daily Times shared more than 6000 times on Facebook and attracting dozens of comments in opposition to the decision.
The story was also shared in the Portuguese media, and the pair were inundated with messages from all over the world condemning the move, Ms Jones said.
Immigration NZ told the Otago Daily Times it could not comment on specific cases but there were general reasons it refused people entry into the country. They included a suspicion a visitor intended to disregard their visa obligations and become an overstayer, or did not meet the character requirements of their visa.
"The most common reason being that we are not satisfied that they have come to New Zealand for the purpose they have stated," said assistant general manager Peter Devoy.
"All decisions must be reviewed by an appropriately delegated officer before being finalised."
More than 3 million international visitors arrived in New Zealand in 2014-15, with 1345 turned away. The most common nationality to be refused entry was Hong Kong, with 115, followed by South Africa (94), Great Britain (89), Taiwan (88) and Malaysia (85).