Alexis, 34, once told police he suffered from an anger-fueled blackout when he shot out a car's tires, but was also known as a quiet man who meditated regularly at a Buddhist temple in Texas and had taught himself to speak Thai.
The defense contractor was killed in a gunfight with police, who have not yet speculated as to a motive for the shooting, which also left several people hurt.
The FBI released two photos of a bald-headed Alexis, an African-American man who weighed about 190 pounds (86 kilos) and stood at 6'1 feet (1.85 meters).
Born in New York, Alexis served in the military from 2007 until 2011, the US Navy said.
"There is definitely a pattern of misconduct during his service," a US military officer, who spoke on condition of anonymity, told AFP.
The officer did not yet know if Alexis had been dishonorably discharged, but his record was clean enough to get hired at an HP subcontractor called The Experts, which worked on the Navy and Marine Corps's Intranet.
Three years before he enlisted, Alexis was arrested in Seattle for shooting out the tires of a car parked near his grandmother's house after construction workers had "disrespected him."
He told police that he could not remember firing the Glock .45 caliber handgun until about an hour afterward, according to a Seattle police report.
Alexis explained to detectives that he was in New York during the terrorist attacks of September 11, 2001 and described "how those events had disturbed him."
Detectives later spoke with his father, who told them his son's "anger management problems" were due to post-traumatic stress disorder and that he had been an "active participant in rescue attempts" after the attacks.
Formal charges were never processed because the paperwork never reached prosecutors, the Seattle Times reported.
"From the outside, he was a quiet person," J. Sirun, an assistant to the monks at the Buddhist temple Alexis attended in Texas, told the Washington Post.
"But on the inside, I think he was very aggressive. He did not like to be close with anybody, like a soldier who has been at war."
"I didn't think he could be this violent," Sirun said. "I would not have been surprised to hear he had committed suicide. But I didn't think he could commit murder."
A former roommate who described Alexis as his "best friend" was shocked by the news.
"I don't think he'd do this," Nutpisit Suthamtewakul, owner of Happy Bowl Thai, told the Fort Worth Star Telegram.
"He has a gun, but I don't think he's that stupid. He didn't seem aggressive to me."
A former landlord, who also frequents the temple, was also stunned by the news and said he'd never seen Alexis get angry about anything.
"Oh boy, I can't believe this," Srisan told the Star Telegram. "He was always very polite to me."
The only hint of trouble was when Alexis complained a couple months ago that he hadn't been paid for a contract job in Japan, said friend Michael Ritavato.
He was also spending a lot of time huddled in his room playing violent video games, Ritavato told reporters outside Happy Bowl Thai.
Alexis spent the bulk of his military career in a fleet logistics support squad in Fort Worth, rising to the rank of Aviation Electrician's Mate, third class, the Navy said.
He received two common awards during his service: the National Defense Service Medal and Global War on Terrorism Service Medal.
The Seattle incident was not the only time Alexis was in trouble with the law, according to a Fort Worth police report.
An upstairs neighbor, who told police she was "terrified" of Alexis after a longstanding dispute over noise, called for help after a bullet flew up through her floor one evening.
Alexis told police the gun went off accidentally while he was cleaning it and that he didn't think it went all the way through the ceiling because he couldn't see any light through the hole.
He was booked on suspicion of recklessly discharging a firearm, but prosecutors said Monday he was never formally charged because they believed it was an accident.
BA/BA