"He hasn't put the weapon down and has been shot," she said.
The man was given immediate medical assistance, and other officers who arrived shortly after had also tried to help, but the man had died.
Fijian news outlet Radio Apna reported the man was believed to be from Fiji.
It reported the man, in his mid-40s, moved to New Zealand "several years" ago.
Police are yet to name the man.
A post mortem and formal identification process are under way.
No one else was injured during the incident, which is the subject of investigations by police, the Independent Police Conduct Authority and the Coroner.
"It's been a really frightening incident for all concerned," said Rogers.
One resident, who spoke to the Herald on condition he not be named, was woken around 1.30am by banging.
He looked out the window to see a man walking from the Carruth Rd direction towards Great South Rd.
He went out to the front deck to see what was happening.
"I saw a guy walking past on the opposite side. He started to smash something - I couldn't see if it was the cars or a house. That's when I rang police."
The first police car had arrived quickly; the man had walked down a driveway so the neighbour couldn't see the shooting unfold, though he heard "about two shots - I'm not sure".
Police had since come to his door to ask for a statement.
A scene examination is being carried out and police are speaking with witnesses.
"Our sympathies are with the deceased man's family," said Rogers.
"We will ensure that Victim Support is available to them and will support them through this difficult process."
Every day police officers were put into complex, fast-moving situations where their lives and those of the public were at risk, and they had to make quick decisions, she said.
"No police officer comes to work wanting to end up in a situation like this.
"Their welfare is paramount to New Zealand Police and we have steps in place to make sure they are well supported."