Phillips' vehicle was found south at Kiritehere Beach on Sunday by members of the public. They informed the family who alerted police on Monday morning.
An extensive hunt along the coastline and in dense bush has failed to find any sign of them.
Paul Phillips says his nephew was homeschooling his children and the family was hopeful he had just taken them out into the bush for a few days.
"We're not sleeping a lot at the moment, obviously we're worried about what is going on," he says.
Thomas had custody of the children and had been looking after them for the last three years, after returning from the South Island when his marriage did not work out.
Paul says Thomas had been farming and done fencing contract work in the South Island, and now worked for his father on his farm. The children's mother was in the Otorohanga - Te Kūiti area at the moment.
Thomas also lived in a house his parents bought him in Otorohanga so the children could go to school, but had decided to homeschool them, his uncle says.
"We're hoping he's just gone and hidden in the bush," Paul Phillips says.
"My brother and sister-in-law are very positive about this, they don't want to think the worst."
He says he naturally feared for his nephew and children when the truck was found by the water.
"The sea was pretty rough down there at that particular time, I think a two-and-a-half metre swell, so they could have been on the rocks, and could have been caught by a freak wave or anything."
His nephew was a competent bushman and a keen pig hunter, he says.
There's nothing specific that would have made his nephew leave, as far as he was aware, he says.
The Eagle helicopter from Auckland has been deployed for the search, as well as three drones operated by Fire and Emergency and a Coastguard plane.
Search and rescue teams were also scouring nearby land including dense bush and beaches. Police were also doorknocking in the Marokopa area.
Waikato West area commander Will Loughrin says thermal imaging drones had been used through the night.
Thomas Phillips' mother Julia says the family is holding out hope her son and the three children will be found soon.