Investigators believe the goal of the assailant was to kidnap Jayme, though Patterson has no apparent prior connection to the family.
Investigators also don't know the conditions under which she was kept in the cabin in the remote Wisconsin community of Gordon or how she escaped.
Jayme told them Patterson wasn't going to be home until midnight, Kasinskas recalled.
Smart, who is married and now 31, said that although the details of Jayme's ordeal have not been released, the fact that the girl "rescued herself" speaks volumes of her strength.
Almost three years ago, Patterson worked for one day at the same meat products facility where Jayme's parents worked - the Jennie-O Turkey Store plant in Barron - the company's president said.
Shortly before 1 a.m. that night, 911 dispatchers got a call during which they could hear yelling, but no one talked to the dispatcher.
"My beloved sister Denice and brother in law Jim can rest a peace, and I keep assuring them Jayme is safe and we will make sure [she is] forever", Smith added in her emotional post.
Closs was released from a Minnesota hospital Friday and is staying in Barron, Wisconsin, with an aunt. Her grandfather, Robert Naiberg, told The Associated Press that Jayme told Federal Bureau of Investigation agents she doesn't know Patterson at all.
Investigators believe Patterson broke into James and Denise Closs' home near Barron on October 15, gunned the couple down and abducted 13-year-old Jayme Closs.
Then, on Thursday, a woman walking her dog in the town of Gordon, about an hour north of Barron, spotted Jayme on the street. Nutter said she was alarmed that the teen wasn't wearing boots or gloves.
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"This is the nightmare case that we all, as parents, family members ... dread", FBI Special Agent Justin Tolomeo said. Nutter went to leave, only to return to the cabin to put on anti-slip cleats over her shoes.
Patterson was arrested the day after Closs escaped.
The teenager was found on Thursday after she managed to escape a man who authorities say killed her parents and then held her captive for three months.
"Right now at this point in time, I feel that it's very, very vital for her to build those relationships with her family because, unfortunately, her family was brutally torn apart", Smart said.
Investigators say there's no evidence of any online interactions between him and Jayme.
"When I was on with 911, I was asking the questions, Jayme wasn't really talking on her own", Kasinskas told CNN.
Charging documents could shed more light on the case.
There will not be a plea in court Monday, according to Patterson's attorneys.
Barron County Sheriff Chris Fitzgerald has said he believes Patterson went to the property with the intention of taking Jayme.
When deputies arrested him, he was out looking for Jayme, Fitzgerald said.