It was standing room only at the town's Sinclair Centre as about 400 people gathered to say their final goodbyes.
Tributes flowed for Ms George, her daughter Pio Raukete, 5, and sons Teuruaa George, 3, and Teiyzshwaun George, 2, who were found dead in a Thomson St house nine days ago.
Police believe the family died from carbon monoxide poisoning after a car in an adjacent garage was left running to keep its battery "ticking over".
Family and friends travelled from the Pacific Islands and Australia to attend the service, which followed a private family funeral on Thursday.
The caskets were carried into the centre by family, friends, and members of the police.
Bishop Mora Pongia from Ashburton's Church of the Latter-day Saints conducted the service, while Ashburton Mayor Angus McKay and members of the victims' families also paid tribute.
Poko Ngaro, one of Ms George's cousins, said Cindy was a devoted and loving mother. She had made Ashburton her home since leaving the Cook Island five years ago, and Mr Ngaro praised the way the community had rallied around the family since the tragedy.
"We're humbled by the support we've received," he said.
Mr Ngaro said the loss was still sinking in, but it had brought the community closer. "It was a pure accident. Mistakes do happen, the key is education," he said.
Bishop Pongia became emotional at times as he described how the church community was coping with the loss of Ms George and her children.
She was a special woman who often arrived early for church because she was so excited to see everyone, he said.
Mayor Angus McKay offered his condolences to the family on behalf of the Ashburton community.
"Cindy and her children did not deserve to be taken so soon," he said.
"The emotional wounds will take time to heal."
