One of the bogus carers also impersonated missing Margaret Fleming, claiming more than £182,000 in benefits in her absence.
Judge Lord Matthews said the couple had caused "immense grief" to Ms Fleming's family as he sentenced them to life imprisonment.
It will be 14 years before they are eligible for parole.
He said: "It seems obvious that the motive for the murder and cover up was financial."
He added: "Precisely how that was accomplished and any other circumstances was not disclosed in evidence and only you two know the truth.
"Only you two know where her remains are.
"That remains a source of immense grief as far as her mother is concerned."
Jones and Cairney have been urged to tell investigators where Ms Fleming's body is, so she can have a proper burial.
Couple denied knowing where Margaret had gone during television interview
Following the teenager's disappearance, the couple recorded a television interview with the BBC in October 2017.
They complained about having to move out of their property to allow police to search for a body - and remain adamant they "had not done anything" to the teenager and that she had run off with a group of travellers.
Cairney claimed on the day he said Ms Fleming disappeared, she had a hospital appointment.
Returning to the property to see flashing blue lights, and fearful of authorities, she ran off, he said.
"I don't know which way she went," he added.
He claimed she "walked right through" the search teams who were tasked with looking for her.
He then claimed she had returned to the house and he had spoken to her on the phone.
He then suggested she had travelled to London, then Poland, and had become a gangmaster of a group who hired out agricultural workers.
Jones asserted she and Cairney had been told by police they had made the teenager up as officers searched their lochside home.
She said she believed there was a conspiracy theory against the couple, blaming a slow police investigation for not looking into details they had passed them.
"I don't understand why things have taken so long, why they haven't done more to find her," she said.
Following the interview, the couple were arrested and questioned by police.
During questioning recorded in October 2017, an abrupt Cairney is seen responding: "No comment," and speaking aggressively to investigating officers.
He is asked by police; "This is a crucial question... I'm asking if you murdered her?"
His response was: "Why is it a crucial question?"
He then says: "You cannot show me anything baby, I know what you are, I know what you're like" to the officer trying to probe him for answers.
What happened to Margaret Fleming?
Ms Fleming moved into the couple's home as a teenager after the death of her father in 1995.
It was said during the trial the circumstances around the move were forged because those closest to her "didn't want her".
It was claimed the last independent sighting of her was at a family event on December 17, 1999.
Suspicions were raised and an investigation was opened after she routinely missed appointments from care workers, eventually leading to a police investigation being opened.
As police zoned in on the couple, they fabricated stories to explain Ms Fleming's absence.
They claimed she was both working as a gangmaster and capable of travelling overseas, and that she was someone with major difficulties requiring a number of benefits.
Officers have never concluded what happened to Ms Fleming.