Investigators have said Patterson's goal was to kidnap Jayme, but he appears to have no connection to the family.
"Probably one of the more hard issues is going to be finding that new sense of normalcy in her life", said Smart, a 31-year-old mother of three.
Jayme had been missing for almost three months Thursday when she approached a stranger near the small, isolated north woods town of Gordon and pleaded for help.
In Jayme's case, law enforcement received more than 3,500 tips, but the town of Gordon, Wis. - where the teen was found and a 21-year-old man was arrested Thursday - was not on their radar, according to the Barron County, Wis., sheriff. "The shotgun was also used ... to shoot open the door at the Closs home on the night of the incident".
He is also accused of kidnapping the youngster.
"The community has been fantastic, and I want Jayme to know that we support her any way possible", said Kari Seelig, with Barron Hometown Pharmacy.
Jayme told one of the neighbors in Gordon who took her in that she had walked away from a cabin where she had been held.
"When we said she was found safe and alive, (there were) tears and lots of hugs", Fitzgerald said.
As an adult she realized they didn't mean any harm, she said. "And the dad I guess, I don't know".
That woman brought Jayme to the home of neighbors Peter and Kristin Kasinskas.
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.
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Federal Bureau of Investigation special agent Justin Tolomeo told reporters: "In cases like this we often need a big break - it was Jayme herself who gave us that break".
The Kasinskas said Jayme's emotions were "pretty flat" while they waited for the police and she refused offers of food and water.
Local teacher Jeanne Nutter was walking her dog when she found Jayme on Thursday.
Both the woman and the neighbour recognised the teen immediately on Thursday due to the enormous public campaign following her disappearance, Fitzgerald said.
'I thought "Good for her, she escaped"', he recalled.
"What a great feeling to have her home", wrote the 13-year-old's aunt, Jennifer Smith, who is the sister of Jayme's late mother, Denise Closs.
'Praise the Lord. It's the news we've been waiting on for three months. "I have accomplished getting over things that trigger me", she said. "So when pictures of missing children pop up in your social media or they come in the newspaper or flash across the screen in the news, or you see a sign above the freeway giving details, don't just think, 'Well, it's not going to me who sees them'".
Patterson was not at home when Jayme escaped, the sheriff added. It was not clear whether he had any prior connection to the family.
They described the 13-year-old as the suspect's "only target" and said Jayme was "taken against her will".
Almost three years ago, Patterson worked for one day at the same meat products facility where Jayme's parents also worked - the Jennie-O Turkey Store plant in Barron - the company's president said.
Attorneys for Patterson called the affair "a very tragic situation" and said they were relying on the court system to treat him fairly.