The 42-year-old Jess was sentenced to 55 years in prison for 2004 convictions in Park County on charges of a sex crime and failure to register as a sex offender. He had an earlier rape conviction in Washington state, according to authorities.
"He may have had it made up in his mind he wasn't going back to prison, one way or another," Linder said.
Linder, who was on the scene of the shooting, said he determined the man shot by the deputy was Jess based on a photograph of the escaped inmate. An autopsy will be conducted to confirm Jess was the man killed.
Jess was working for the Deer Lodge prison's motor vehicle maintenance on a service call when he escaped Monday. His vehicle was found about 1 ½ miles from the prison, leading prison officials to believe he had fled into the rugged area nearby covered by trees and brush.
A ground and air search turned up no sign of him. Jess was not a problem inmate and had worked for the prison's motor vehicle maintenance since 2006, prison officials said.
Authorities were first alerted to his possible presence in the Billings area when a person came into the sheriff's office Friday morning to report being contacted by Jess, Linder said.
A phone call from Jess to the witness was traced to a pay phone at the Wal-Mart shopping center.
As authorities converged on the scene, a report came in of a green Jeep stolen from the Deer Lodge area, Linder said. A deputy spotted a Jeep matching the stolen vehicle description leaving the Wal-Mart parking lot, and several deputies used their vehicles to block it in as Jess tried to leave the shopping center, Linder said.
Jess, who was holding a gun, had locked himself in. For the next 15 to 20 minutes deputies tried unsuccessfully to persuade him to come out, Linder said.
When Jess moved a gun toward one of the deputies the deputy opened fire.
"Deputies were yelling at him 'Put the gun down, put the gun down,'" Linder said. "I believe I heard one of them say 'Don't do it,' and shots were fired."
The name of the deputy involved was not released. Linder said he had been on the force for about 15 years.
Under Montana law, a coroner's inquest will be held in coming months to determine if the shooting was justified.