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About 65 Kiwis have travelled from Sydney on to Melbourne since the arrangement began on Friday, and more were expected to arrive on Monday.
Some have also arrived in Hobart, Adelaide and Perth, where they will be required to undergo 14 days of hotel quarantine.
Mr Andrews maintains the federal government did not inform him New Zealanders were entitled to travel beyond participating states and territories.
"People turned up without us knowing. People turned up without the WA government knowing. People turned up, I assume, without the Tasmanian government knowing," Mr Andrews told reporters on Monday.
"These bubble arrangements were presented very clearly as just that - a bubble - and that if you wanted to be part of it, you could.
"We said no, we don't think we should be at this time, however, it seems we are in it so we will make the best of it."
He said the Department of Health and Human Services' website had been updated on Sunday night to reflect the situation.
"We will provide the best health advice because, despite the fact that we didn't want to be in the bubble, it seems like the bubble applies to every part of our country, not just those that said yes," Mr Andrews said.
He said New Zealanders arriving in Victoria would not be required to quarantine due to the low number of coronavirus cases in their home country.
But they will have to comply with the state's coronavirus restrictions, which were eased on Monday.
People living in Melbourne can now travel 25km from home and they have greater freedom when it comes to social activities and exercise.
Hairdressers and other industries can also operate for the first time in months, though retail and hospitality will have to wait until November 2 before they can reopen.
Mr Andrews said the date could be brought forward if case numbers remained low.
He hit back at federal Treasurer Josh Frydenberg, who described the state government as having a "callous indifference" to small businesses and called for restrictions to be lifted quicker.
"It's all about the politics with this bloke, isn't it? That's all he does. He is not a leader, he is just a Liberal," Mr Andrews said.
He defended the government's decision to take a safe, steady approach.
"These are not easy decisions, they are decisions that have to be carefully weighed up," Mr Andrews said.
In regional Victoria, up to two people plus dependents are now allowed to visit homes once a day, while hospitality venues can increase their capacity to 70 people outside and 40 people inside.
The regional city of Shepparton, which has been the centre of a COVID-19 outbreak, will not be able to host 40 people indoors for the time being.
Melbourne recorded four new coronavirus cases on Monday, bringing the city's 14-day rolling average down to 7.2.
Three of the new cases are members of the same household, in the local government area of Hume, who are connected to an outbreak at Box Hill Hospital.
The fourth is a Moonee Valley resident who had the virus in July, but appears to still have traces of coronavirus in their system.
"We need to exclude the possibility that it is reinfection with a new virus," Victoria's Chief Health Officer Brett Sutton said.
An aged care resident in his 90s is the latest virus fatality, bringing the state's death toll to 817 and the national figure to 905.
There are 15 cases for the fortnight up to Friday which have no known source, including a child in the Royal Children's Hospital oncology unit.