The discovery of the men was the result of an operation by INZ focused on the construction industry.
INZ deputy head of Immigration Stephen Vaughan said one employer was involved in the case, but declined to reveal more details. He also declined to comment on charges but said inquiries were ongoing.
He said a visit to the site was part of INZ's proactive approach to ensure all employers and migrant workers in the sector were aware of their rights and obligations. Cases like this were not uncommon, he said.
'Behaviour we will not walk past'
"As part of our construction sector strategy, we're actually looking to get better information and understand some of the challenges in the sector and working along employers to educate them about the legal obligations and ensure foreign nationals are actually working lawfully in New Zealand," Vaughan said.
"We do on occasion visit construction and other sectors and their workplaces and find some really great examples of work practices from employers and employees, but on this occasion, the visit we made yesterday, there was some behaviour that we will not walk past."
Migrant Workers Association Aotearoa president Anu Kaloti said her organisation was trying to find out more details and offer any support needed to the men.
Kaloti said more accountability was needed from employers rather than punishing the migrant workers.
"It doesn't matter how many levels of sub-contracting we have, there needs to be a system where each and every tier can be accountable so these workers should not have been allowed to be unlawful in the first place," she said.
"Obviously they were needed here because they were working, so why weren't they given the correct documents? ... they should have been documented with [the correct documents] rather than made unlawful workers ... they should never have been put in that precarious situation of being unlawful in this country."
Education packs for employers
During the operation, INZ staff have also met with lawful migrant workers and conducted checks to ensure they are being treated fairly by their employers.
INZ said education packs had also been provided to employers to ensure they had all the information they needed about their obligations.
Vaughan said employers could face consequences if they did not observe the rules, and foreign workers should also abide by the laws.
"Any employer who exploits individual employees is actually committing an offence against the Immigration Act, which carries a significant penalty of seven years' imprisonment or a fine not exceeding $100,000, or both," he said.
"The first thing is that employers have certain obligations when employing migrant labour and also migrant workers have a responsibility to ensure that they remain lawful while they're in New Zealand and working, so there are clear messages for both employers and employees."
RNZ has approached the Chinese consulate for comment.
- RNZ