He said that he had had to borrow $5000 from his parents to pay the IRD before it was satisfied he could leave the country. His wife, Diane, told the Herald from the Cook Islands that the IRD sent reminder letters to the wrong address.
She was audibly upset when speaking with the Herald, and said the arrest had come as a huge shock to the family.
Puna has lived in the Cook Islands for 13 years, she said. "We never had any contact from IRD about the whole thing," she said. "They were sending reminders to the wrong address."
He described the day he got arrested as the worst of his life, "if you don't count deaths".
Puna, who said he came from a family of "high achievers" said he was pulled aside by Customs staff and initially thought it was about his emergency passport, which he had obtained after losing his original passport.
"I sat there, ate my three pieces of KFC and the police came and said I was under arrest for my student loan. I looked around; I thought it was some kind of joke."
Puna said he sat in a cold police cell for more than seven hours. "That's my first time in a police cell. It was unbelievable," he said. "I don't think I'm a criminal."
The father of five daughters said his salary was about $35,000 and his mistake was that he had not contacted IRD when a payrise took him over the repayment threshold five years ago.
Though he was committed to making repayments he said he had a $300,000 mortgage to think about.
Puna accepted he would owe the IRD money until the day he died.
He said outside court the authorities had used him as an example and he did not think his treatment had been fair.
"It made me feel like a criminal."
He said his plan was never to rack up a huge debt and then ignore it after graduating but accepted he was in the wrong for not keeping in touch with the IRD.
When he returns to the Cook Islands, Puna said he wanted to make others aware of their financial responsibilities.
Cook Islands Prime Minister Henry Puna with John Key at the Pacific Islands Forum in 2013.
"I'm going to try and figure out something so others don't have to go through what I went through," he said.
An IRD spokeswoman said the agency could not respond to specific questions about the case due to privacy laws.
A law change in March 2014 means student loan borrowers who are well behind on repayments and ignore requests from Inland Revenue may have an arrest warrant issued, stopping them from leaving New Zealand until they resolve their arrears.
Inland Revenue has tracked a small number of overseas-based defaulters but, despite the controversial policy generating headlines, until now no arrest warrant had been issued.
Tertiary Education Minister Steven Joyce said he was also unable to respond to specific questions about the case as it was before the courts.
When asked if the arrest was considered a success for the Government's student loan recovery initiatives, he said:
"Our preference is that people just meet their obligations and that's the important thing because you can't forget that these people have had the benefit of loans from the tax payers to be educated.
"They have made a commitment to pay the money and in some cases, not all cases, they have gone offshore and chosen to forget this."
Arrest was the "last resort", he said. "If people refuse to do anything there has to be some consequences."
Mr Joyce said there were hardship allowances for people unable to make repayments, but they needed to make contact with IRD to organise such arrangements.
An IRD spokesman said its powers to arrest at the border were used as "a very last resort", and followed strenuous efforts to contact the borrower and make repayment arrangements.
Serious defaulters are first contacted to discuss repayment options and are given time to repay some of their loan. Relief from repayments can be granted for hardship reasons, but the man arrested had not made any such application.
An arrest warrant can be issued if a court is satisfied that the person has committed the offence of knowingly avoiding student loan repayment obligations, and is about to leave NZ.
A district court can then make subsequent orders that include paying the amount in default, making arrangements for payment, providing security for the payment, not leaving the country without permission, and surrendering travel documents or tickets.
An information-sharing agreement with the Department of Internal Affairs also alerts Inland Revenue when defaulters apply for a New Zealand passport.
According to the latest student loan scheme annual report, produced by the Ministry of Education, the amount repaid directly by overseas-based borrowers was $184.7 million in 2014/15, up from $158.1 million the previous year.
The New Zealand University Students Association acting president Laura Harris was concerned by the court case.
"It's really concerning for the large number of these students that want to come home and visit their families and parents, and come to tangis and weddings and funerals. People are going to be scared to come home," she said.
She said that the repayment system was flawed, and should be based on a debtor's income not the amount owed.
"The way that you repay the schemes is based on your student loan and not your income. The system should encourage them to pay loans instead [of] really harsh penalties."