Police initially said the vehicle backed up toward officers "in an aggressive manner," but later admitted that bodycam video showed the vehicle was moving forward as officers approached. Oliver's partner told jurors he didn't believe his life was ever in danger.
Investigators said no guns were found in the vehicle. Oliver was fired from the Balch Springs Police Department days after the shooting.
Around 7:15 p.m. Wednesday, the jury sent out a note asking the judge what do they do if they can't reach a verdict, CBS Dallas / Fort Worth reports. The judge replied they have all the information they need to make a decision. If jury can't come to a decision, it will be a hung jury and a new jury would have to be picked to come up with the punishment.
During the sentencing phase, people who say they know Oliver best – co-workers and friends – painted a picture of a man who is well-loved and respected in the community, CBS Dallas / Fort Worth reports.
Billie Gorwood, who once had Oliver as a tenant, begged the jury for leniency. "He wants to help and he wants to protect. And this tragedy has gone against everything, everything that Roy believes in."
Edwards' stepmother, Charmaine Edwards, took the stand after the verdict was read Tuesday. "It's just trying to get through life without him now, and it's hard because he had a promising future," she said.
When the verdict was read Tuesday, gasps echoed around the courtroom. Edwards's relatives sobbed and hugged prosecutors, waved their hands in the air and proclaimed "Thank you, Jesus!"
"I just want to say I'm happy, very happy," Edwards father, Odell Edwards, said outside the courtroom. He said it had "been a long time" since he felt that way.
The jury, which featured two black members out of 12 jurors and two alternates, acquitted Oliver on two lesser charges of aggravated assault stemming from the shooting.
It's extremely rare for police officers to be tried and convicted of murder for shootings that occurred while they are on duty. Only six non-federal police officers have been convicted of murder in such cases - and four of those convictions were overturned - since 2005, according to data compiled by criminologist and Bowling Green State University professor Phil Stinson.
Edwards' father has also filed a civil lawsuit in connection to the shooting.
(© 2018 CBS Interactive Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)
