"Before we knew it, the boat was under… and we were just hanging on."
With their radio failing to work, his father was luckily able to reach for a mobile phone stored in a water-proof case and call his wife for help.
Joshua panicked at first, before calming himself.
"For the first 10 minutes, I was freaking out a bit… it wasn't a situation I wanted to be in," he said.
"But then we just kept talking to each other… I kept trying to make Dad laugh."
He estimated the pair, fitted with lifejackets, spent nearly an hour clinging to the boat, which was floating just 20cm above the water level.
"Dad started getting mild hypothermia – so we were just lucky help came when it did."
Local volunteers reached them first, before Nelson Marlborough Rescue Helicopter took his father to hospital.
"The paramedics checked Dad for hypothermia… I was a bit warmer when they turned up so I just wanted them to focus on him."
Yesterday, the family was trying to settle back into their summer holiday.
"The volunteers were awesome and we really appreciated what the paramedics did for us – I shaked the hands of every one of them I could."
The helicopter duty pilot said he didn't get the chance to talk very much to Gary Jamieson during the trip to the hospital, but said the whole team was relieved at the outcome.
"It could have been far more serious and they were probably lucky there were a few other vessels and people fishing in the vicinity."
Police said the incident should be a timely message for boaties.
"This was another great rescue by our local volunteers and a good reminder to check your safety equipment before heading out," senior constable Jonathan Davies said.