Mr Pevreal said Mr Milne and his wife, Janette, had three biological sons but also fostered many more children over the years.
"Outside of work, Terry was also a great family man with a big heart," Mr Pevreal said.
"At this time, our thoughts are with Terry's wife and children, and his large extended family."
In a written tribute, Mr Pevreal also said Mr Milne was a highly valued and long-standing employee.
"He was very passionate about his work and our company," Mr Pevreal said. "He took pride in everything he was involved in. Clients and other subcontractors often requested him by name.
"Terry also loved the snack box. We will miss hearing the sound of him searching for a treat."
People in neighbouring properties reported hearing a loud explosion on Monday.
Emergency services were sent to the earthmoving company at about 1pm but efforts to revive Mr Milne were not successful.
WorkSafe NZ was investigating the incident and Mr Pevreal said it'd be inappropriate to discuss the accident in more detail.