The Fleets' deaths came after Raymond Fleet became involved in a methamphetamine manufacturing enterprise which did not return the yield those who ordered it anticipated.
At the jury trial, it was emphasised James Fleet had not taken part in manufacturing the drug but had been "in the wrong place at the wrong time" when he and his uncle were forced into the vehicle that took them to the place where they were to lose their lives.
Pulemoana was jailed for life with a minimum non-parole period of 14 years.
His legal team then filed an application with the Supreme Court in October arguing that one of the jurors had been in an antenatal course run by James Fleet's mother Bronwyn (Bron) Fleet 14 years prior, and that person would have been biased.
The Supreme Court has now rejected that argument in a decision released today and did not identify a miscarriage of justice.
When Pulemoana's team first appealed to the Supreme Court, James Fleet's mother Bron Fleet told the Rotorua Daily Post at the time she accepted he had a legal right to appeal.
"I can do nothing but trust in our justice system to make the appropriate finding."
She said every day was a "challenge" to manage the grief of losing James and to keep their family strong and together to support each other.
"Every court hearing is like pulling the scab off a wound that's trying desperately to heal, it's devastatingly painful. I hope one day soon that this will finally be over and James can rest peacefully knowing that those who took his life are held accountable."
Pulemoana stood trial with co-accused Mikaere James Hura, 21, who was found guilty of the manslaughter of both men and was jailed for six years.
Martin Hone pleaded guilty to the men's murders and was sentenced to life with a minimum non-parole period of 20 years.