"We didn't want him to hear us crying while he was dying, we wanted him to hear our voices so we started talking to him quietly, telling him his name and that he had a sister," Mrs Ogg said.
"Next thing he's gasping more regularly and starting to move and cry."
After Jamie started gasping more regularly and took breast milk off Mrs Ogg's fingers, she and husband David had to persuade the doctor to come back to look at him.
But once in the room, he started explaining to the couple how Jamie had died. "And we're saying, 'Okay, so when he's breathing it's just a reflex?'. And he's like, 'Yep, you're not seeing what you think you're seeing."'
After two hours the shocked couple had stopped believing what the doctor said and told him Jamie was not dead.
"When I pulled him off my chest he was startled and waved his arms around and tried to cry again, and the doctor goes 'oh s***'."
The amazing recovery has made the Oggs - who moved to Nelson from Australia last November - into strong advocates of skin-on-skin contact with newborn babies.
The contact, known as kangaroo care, is said to normalise temperature, heart rate and respiratory rate, increase weight gain and reduce infections for pre-term babies.
Mrs Ogg said she could see the results instantly when she lifted Jamie and Emily from their hospital incubator.
"Once you settle down with them they get a better blood pressure, a more even, regular heartbeat, their body temperature settles and they go into REM - deep sleep," she said.
Although it was a natural reaction to hold her baby for what she thought was going to be the last time, Mrs Ogg believes skin-on-skin contact saved Jamie's life.
"If he didn't have the warmth he would have died. I think he needed it; they come out and just imagine you're in this warm, soft, quiet environment and next thing it's freezing cold, bright lights."
Two years on, the event still weighs on her mind sometimes and she finds it hard to believe Jamie escaped brain damage.
"David and I always said to one another if there's anything wrong as a result of this we'll deal with it when it happens. If there's nothing wrong we've wasted our time worrying, and if there is, worrying wouldn't have helped anyway."
But both Jamie and Emily are developing like other children their age. Their family has also grown - brother Charlie was born last April.
That was not without drama, though, after he tried to come at 20 weeks. But after some serious work to make sure he didn't, Mrs Ogg then had to be induced at 38 weeks. He was born a healthy 4.5kg.
Neonatal Trust chief executive Michael Meads said skin-on-skin contact was very important in the bonding between baby, mother and father.
"The skin-on-skin contact has lots of different benefits, bonding, body heat, so I'm a huge advocate."
Hospitals around Australia encouraged the "kangaroo cuddle", Mr Meads said. It was particularly important for premature babies who had been in an incubator.
"So from a mum and dad's perspective, if you can imagine having a baby and not being able to cuddle your baby for months, once they get to that kangaroo cuddle stage it's a pretty critical stage of growing and bonding."