The man at a Mt Wellington coolstore who tested positive for Covid-19 worked night shifts, a factor which may have helped limit the number of colleagues who have since fallen ill.
A union rep says the outbreak could have been much worse if the employee had been exposed to more people during the day.
Eleven confirmed cases are now linked to the Americold plant as a community transmission cluster worsens across Auckland.
Director general of health Dr Ashley Bloomfield yesterday confirmed 13 new cases in the community, all linked to a family of four in South Auckland, taking the cluster to 17.
Three of the new cases are Americold workers, while seven others are family of infected plant staff.
Two of the company's factories have been shut down on advice from the Ministry of Health.
As workers isolate with their families to prevent further transmission, First Union secretary Jared Abbott said there were also concerns for their financial future.
Americold managing director Richard Winnall said the company was "absolutely committed" to its employees.
It had decided to extend a further 20 days of sick leave entitlement to any worker impacted by Covid.
"We sought to put that in place in NZ yesterday as soon as the latest outbreak came to our attention so there will be no disruption to employee pay."
Winnall said the outbreak was unsettling for staff. About half the Mt Wellington plant's workers were yet to hear whether or not they were infected.
"It's not good. There's a lot of people awaiting test results, they've got families. There's a lot of anxiety and concern."
Winnall confirmed there had been an outbreak in the past week of two cases at the company's Melbourne facility.
Surface testing was under way at the coolstore to determine if the virus could have been brought into the country on refrigerated goods.
However, he was adamant there was no Melbourne link with the Mt Wellington cases. He stressed there were no shipments from the Melbourne plant direct to the company's Auckland factories and the positive Australian cases worked on a completely different supply chain.
Bloomfield agreed the risk was "highly unlikely".
"Almost certainly the most likely explanation is person-to-person transmission, but we're wanting to rule out the coolstore link."
Auckland was plunged back into alert level 3 lockdown on Wednesday after the ministry revealed that the four South Auckland family members had tested positive.
There is currently no known link to overseas travel or managed isolation, and the source of infection is unknown.
One of the four worked at the Mt Wellington plant and another at Dominion Rd company Finance Now.
Bloomfield said two new infections linked to Finance Now had been confirmed. One was an employee who was admitted to North Shore Hospital on Wednesday but had since been discharged. The other was a relative of that employee.
In a statement, Finance Now chief Phil Ellison said the company was focused on supporting staff, who were now working from home.
A testing station had been set up at the company's Mt Eden office to provide rapid testing for staff and their bubbles. Staff had been offered extended sick leave if affected by the virus.
"The welfare of our staff is our absolute priority, and we are doing everything we can to support them and their families, as well as to support the wider public health response and do our bit as part of the team of five million."