He says she has already met with an aunt and will be reunited with her other relatives on Friday night.
Another aunt, Sue Naiberg Allard, posted that Jayme got "the most awaited hug ever" when she returned home.
Jake Thomas Patterson was arrested on two counts of first-degree homicide and one count of kidnapping, police said on Friday.
"These funds are going to go towards the journey with the family as they help Jayme through whatever it may be...driving to take care of her, taking her to the clinic, medical costs or anything", said De Andriano.
Patterson's lawyers Charles Glynn and Richard Jones said in a statement they consider the situation "very tragic" and that they are relying on the court system to treat their client fairly.
Within minutes, Patterson was pulled over and jailed on kidnapping and homicide charges for what authorities said was his meticulously planned shotgun attack at the girl's home in October.
Barron County Sheriff Chris Fitzgerald said investigators are trying to figure out what happened to Jayme during her captivity.
"I thought, 'Good for her she escaped, '" he said.
Naiberg, Jayme's grandfather, said he spent a few hours with her on Friday and she was largely silent.
The Kasinskas said Jayme's emotions were "pretty flat" while they waited for the police and she refused offers of food and water. "She said she did not know him".
The cabin is in Eau Claire Acres, about 10 miles outside the tiny town of Gordon, in the dense evergreen forests of north-western Wisconsin.
A woman who has a cabin nearby was walking along the isolated road when she saw Jayme on the cold evening, just about dusk, without a coat or gloves.
"The suspect was out looking for her when law enforcement made contact with him", Mr Fitzgerald told a news conference, adding police were not seeking any other suspects in the case at this time. Investigators were still interviewing her, and she was "doing as well as circumstances allow", he said.
"I think hope helps you get through the day.it makes it easier", Simmers said.
"My kids and I - we went downstairs", she said.
Patterson took measures to avoid leaving evidence at the scene, including shaving his head beforehand, and a shotgun was recovered from the home where Jayme was believed held, Fitzgerald said. It appears he has been living in the family cabin; property records indicate his father still owned the place in October.
Unemployed Patterson had no previous criminal history and was not on the radar of police. The sheriff said he didn't know whether Jayme had been physically abused.
Police believe Patterson - said to have hidden the girl in the home he grew up in - killed the Wisconsin couple because he wanted to abduct their daughter.
Over the past few months, detectives pursued thousands of tips, watched dozens of surveillance videos and conducted numerous searches for Jayme, including one that drew 2,000 volunteers but yielded no clues.
The president of the Jennie-O Turkey store in Barron, where James and Denise Closs had worked for decades, said Patterson had been an employee for a single day three years ago. Girls ages 12 to 17 are most commonly abducted.