He added that the 36-year-old shooter's nine-year-old son Hayden and five-year-old daughter Harper were in the back of her SUV at the time.
Rahme was the target of an anonymous online attack posted on Wednesday and since deleted, DailyMail.com can confirm.
"This little girl has no self-respect and no morals. She dates married men who have children and she doesn't even want or like kids," the vicious post attacking Rahme read.
"Her character speaks enough for her. Remember homewrecker, that karma is a b---h, just like you. You will get what you deserve," the screed went on, posted to a website that ostensibly identifies "homewreckers".
Two hours after Rahme was shot, deputies found the suspect SUV locked and running with Edens and her two children inside, each dead from a single shot to the head or neck about seven miles away in Easley, Pickens County Chief Deputy Creed Hashe said.
Hashe called it a "graphic and horrific" scene.
A .40-caliber handgun was found inside the SUV, but Hashe and the coroner have not said who fired the shots. A similar gun was used to kill Rahme, authorities said.
Rahme had called police twice less than three weeks ago to ask how she could deal with harassing text messages, phone calls and online postings from Edens, Thomas said.
Edens' estranged husband had called Easley police on Wednesday to ask them to check on their daughter shortly after he received a disturbing text message from Edens and the two had been in court to discuss custody of the five-year-old girl, authorities said.
The officer who went to the home found the family planning to eat popcorn and watch a movie. One of the children was speaking to the husband, according to the police report.
The officer asked Edens if there was any chance she could get back with her husband and she said instead she was going to expose his year-long affair in court, the police report said.
Rahme worked with Edens' husband, Thomas said. He refused to give any other details about their relationship.
Thomas said authorities had no indication Edens was planning violence before the shooting.
"There is some indication that about the time of the custody decision that she had some sense of inflicting violence either on the children or on herself or both. But that wasn't discovered until after she was discovered last night," Thomas said.
Greenville investigators are trying to determine if Edens was waiting on Rahme or followed her into the parking garage under the apartments. Rahme was found dead in the driver's seat of her car, authorities said.
Thomas said the tragedy of the shooting touched several families.
"It is important to remember there are fathers who have lost children to this senseless violence and our heart goes out to them," Thomas said.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call 111.
If you need to talk to someone, the following free helplines operate 24/7:
DEPRESSION HELPLINE: 0800 111 757
LIFELINE: 0800 543 354
NEED TO TALK? Call or text 1737
SAMARITANS: 0800 726 666
YOUTHLINE: 0800 376 633 or text 234
There are lots of places to get support. For others, click here.
