The family were alerted when an 8-year-old boy - one of the four children - yelled "fire, fire, fire'' and they ran outside.
The children's mother thought her young daughter was still inside so re-entered the burning building but was called back when the girl was found safe outside.
The woman suffered smoke inhalation and was treated by ambulance paramedics at the scene.
"The fire was so big, huge,'' Ms Tuialii said. "I'm so happy they got out because it was so bad, so much smoke everywhere, everywhere. I think if they didn't get out quick it could have been very bad.''
The family was too distraught to talk to media as they walked around the wreckage of their family home this afternoon.
Papatoetoe Fire Station Senior Station Officer Terry Jenner said the fire had been started by a child playing with a lighter under a bed.
It was unclear whether there were smoke alarms because "every ceiling in the house is down on the floor''.
Police said the incident highlighted the importance of ensuring matches and lighters were always kept out of reach of children.