But the federal government, which is responsible for worldwide borders, has repeatedly stressed the program is working as it should, with the arriving travellers able to move through the country subject to state's quarantine restrictions like any other Australian citizen.
"Currently the Victorian borders are open", it says on the website.
Some have also travelled to Hobart and Perth, where they will be required to undergo 14 days in hotel quarantine.
Victoria's Premier Daniel Andrews hit out at the Federal Government, saying he - along with his counterpart in Western Australia - had "absolutely no idea" travellers from New Zealand were entering their states, despite opting out of the travel bubble arrangement.
Three flights from New Zealand touched down at Sydney Airport earlier on Friday carrying worldwide passengers who, for the first time in seven months, will not need to quarantine upon arrival.
The Victorian government website tells potential travelers that they should not enter the state if they have symptoms of coronavirus.
"I'm not going to be quarantining people that came from a low virus community, and we just have to make the best of this".
But officials wanted to have a "conversation" with the passengers from New Zealand to ensure they knew what the specific rules for the state of Victoria were.
"Three of the travellers did not cross the border into Victoria and remain in NSW, and one who was in Victoria returned to NSW today".
US in no hurry to develop digital dollar: Fed's Powell
Powell said the Fed's primary goal is to examine the impact of the digital dollar on the American economy. The Fed has faced plenty of criticism for its reluctance to digitalize the US dollar.
"But I do not think it is unreasonable for us to be concerned if a whole bunch of people from another country turn up in Melbourne when we were of the view that we were not part of that arrangement".
"The trans-Tasman bubble is the first in what we need to do to reopen our nation", Mr McCormack said.
In a media statement yesterday, Air New Zealand said fares beyond Sydney were not able to be booked via the airline due to Australian state restrictions.
Dr Beirman said he didn't believe the bungle would stop future travel bubbles from occurring but Australia needed to "approach them more systematically".
According to the ABC, Mr Andrews wrote to Prime Minister Scott Morrison on Saturday, requesting for new arrivals from New Zealand to be prevented from boarding internal flights from New South Wales to Victoria.
"It beggars belief that once again, the Federal Government seeks to avoid responsibility in this manner". Other Australian states are expected to sign up to the plan in the coming months.
It's been less than 72 hours since the first flight from New Zealand landed in Australia, but after a turbulent weekend - the future of travel bubbles may already be about to burst.
People in Australia must stay at least 1.5 metres away from others.