Charlie's aunt Marissa McAllister said the family requested privacy while they grieved. "We're all deeply saddened.''
Charlie's parents Robbie and Lisa posted photos of their son to their Facebook pages last night, attracting a string of tributes.
"Words cannot express enough,'' Misti Tatana wrote. "You, Lisa and Zac xxx You're all in our thoughts and hearts.''
"So so sorry to hear of your loss,'' Rodger Dawson wrote. "Our thoughts are with you all.''
The boys had been visiting the farm. The owner of the property declined to comment.
Charlie's parents were being assisted by family and Victim Support.
Wallacetown Volunteer Fire Brigade officer in charge Brendan Hamilton said the quad bike was lifted off Charlie by the farmer who owned the property.
By that stage Charlie had already been trapped under the vehicle for up to 10 minutes.
Charlie's brother alerted the landowners to the tragedy, he said.
"The farmers and the neighbours were attempting to resuscitate him, and then we took over when we arrived, then the ambulance took over from us.''
The creek was situated at the end of a paddock at the back rear of the farm, Mr Hamilton said.
Fire service staff drove the ambulance to Southland Hospital so St John staff could continue to work on Charlie en route, Mr Hamilton said.
The residents of Wallacetown and Lorneville were a tight-knit community, he said.
A spokesman for WorkSafe New Zealand, the Government's workplace health and safety regulator, said an investigation was underway because the incident occurred at a workplace.
Federated Farmers health and safety spokeswoman Jeanette Maxwell said the organisation suggested that under-16s didn't use adult-sized quad bikes.
"Adult bikes are huge, a little person won't be capable of riding one as they just aren't tall enough.''
- additional reporting Otago Daily Times