Acting Premier Jacinta Allan confirmed all three locally acquired COVID-19 infections reported on Monday are linked to the outbreak, which was seeded by NSW's northern beaches cluster.

An additional separate case was diagnosed in hotel quarantine, taking the total number of active cases in Victoria to 36.

There were 32,468 tests processed on Sunday, up from 22,477, and about another 10,000 are already in the laboratory.

"It's a very strong set of numbers," Ms Allan told reporters, noting NSW also had gone without a new locally acquired coronavirus case over a 24-hour span for the first time in almost three weeks.

The jump in testing figures came even as some sites temporarily closed while struggling to cope with a surge in demand driven by returning Victorians.

More than 60,000 Victorians rushed back from NSW as a hard border between the two states came into effect on Friday night. All of them needed to be tested.

It has led to long lines at testing facilities, forcing some sites to extend hours and the recalling of staff from holidays.

The total number of sites has increased back beyond 200 on Monday, and Ms Allen said the increased capacity was starting to ease delays.

But half a dozen facilities including the Alfred Hospital, Heidelberg Repatriation Hospital and several Monash Health sites were reporting wait times of more than two hours by Monday afternoon.

In many cases, Ms Allen said those arriving at busy sites were being turned away and sent to nearby locations.

Meanwhile, thousands of Victorians who missed the brief window to return to Victoria before the NSW border slammed shut are still waiting to hear back from authorities.

Ms Allen said 2200 applications have been received for an exemption to cross the NSW border, but just 175 have been processed to date.

They are taking 24 to 48 hours to consider, with priority given to emergency medical and compassionate cases.

Despite Monday's encouraging figures on either side of the border, Ms Allan indicated Victoria would not rush to reopen to NSW.

Agriculture workers who live and work between NSW and Victoria and are not covered by existing border bubble arrangements can now apply for a permit.

The Victorian government on Monday announced the immediate rollout of the permit, with those workers only allowed to leave their accommodation for takeaway, bathroom stops, medical care, coronavirus testing or an emergency.

The state's list of coronavirus exposure sites also continues to grow, with Puffing Billy joining the watchlist.

A case visited the popular tourist attraction's Lakeside Station at Emerald Lake on New Year's Eve from 3pm to 5pm.

Anyone who attended the site at those times should monitor for symptoms, and undergo testing and isolate if they develop.

The same advice applies to worshippers who visited a Sikh temple at Keysborough in southeast Melbourne on New Year's Day from 2pm to 5pm.

Australian Associated Press