A Fire in Minnesota. An Arrest in Mexico. Cameras Everywhere.

The A.T.F., which is tasked with investigating arson cases, released photos of suspects, offering $5,000 for helpful tips from the public. A video of Mr. Felan “went viral,” leading to “several tips, including from individuals who wish to remain anonymous,” an A.T.F. agent said in a court document. (The A.T.F. has also used facial recognition technology, including the app Clearview AI, to identify unknown people, according to reporting from the Government Accountability Office and BuzzFeed.)

Mr. Felan and Ms. Yousif could not be reached for comment. Mr. Felan’s lawyer declined to comment as the case is pending, and Ms. Yousif’s lawyer did not respond to multiple attempts to reach him. This report is largely drawn from government documents and sources, and based on the account of their lives there, they were likely panicked. Mr. Felan had previous legal troubles.

And Ms. Yousif was approximately seven months pregnant.

So they drove, heading south on Interstate 35, a highway that runs down the middle of the country, stretching from Duluth, Minn., on Lake Superior, to Laredo, Texas, on the Mexican border. They had made their way through Iowa and just hit the northern part of Missouri, 300 miles from Rochester, when police first caught up with them.

A warrant had been issued for Mr. Felan’s arrest, allowing the authorities to ping his cellphone to locate him. According to a court document, late on a Monday night, more than a week after the events in St. Paul, local police in rural western Missouri, who were asked to go where the phone was pinging, stopped a black S.U.V. registered to Mr. Felan. Ms. Yousif was driving, and said she didn’t know where Mr. Felan was. The police let her go.

Ms. Yousif was then charged with helping Mr. Felan flee, and the A.T.F. put out a new request for help, setting the reward at $10,000: “We’re asking the public to be on the lookout for the couple along the Interstate 35 corridor.”

Over the next week, police kept pinging the location of Mr. Felan’s phone but kept missing him. According to a court document, he sent a message to his brother in Texas saying he was turning it off between messages, worried about being tracked; the couple eventually bought new phones.

They bore west, through Kansas and Oklahoma, making their way toward Mr. Felan’s family. His mother and brothers had heard about the manhunt and were sending one another worried Facebook messages. At some point, the couple exchanged cars with Mr. Felan’s mother.