After three episodes of assuming that Cyrus killed Vargas, Tom finally confessed to the murder himself, but why did Tom kill Frankie Vargas on Scandal? His motive likely has to do with getting revenge on Cyrus for turning him away and permanently rejecting him, but it's safe to say that Cyrus probably had nothing to do with Tom killing Vargas, at least not intentionally. Not that I wouldn't put it past Cyrus to commit murder, because he's Cyrus Beene after all, but he also would have never hurt someone he truly cared so much about.
The way I see it, Vargas was like Cyrus' next Fitz, a man he seemed happy to work for, and when Tom brought up the idea of killing him, Cyrus told him to back down. So as awful as Cyrus is, Tom's reason for killing Vargas on Scandal wasn't about getting orders from his former lover, despite his recent confession. Instead, it was likely due to Tom's unhealthy obsession with Cyrus.
Tom killed Vargas on Scandal because he thought it would work in Cyrus's favor and now that Cyrus is totally finished with him, he confessed to the crime to get back at the would-be new president. Hell hath no fury like a lover scorned, right? Well, throw in the fact that said lover is also a highly skilled and sociopathic killer and it's a recipe for disaster.
In the promo for Episode 4, it's clear that something big is going to come out that could possibly exonerate Cyrus and get Olivia in his corner. Or, at the very least, to help her finally believe his innocence. It's no real shocker that once upon a time, Cyrus and Tom had a friends with benefits situation going on. But Cyrus has somehow settled into married life with his husband and little girl, and when he was running in the presidential race with Vargas, he seemed like he was going to start doing some good for once. Then, he had that girl from the campaign beaten and it was like, "Oh there you are, Cyrus."
Still, even though he and Vargas heatedly clashed over that unfortunate situation, he made it clear that he didn't want anything to happen to Vargas. But Tom, ever the dutiful lover, obviously thought it was the right thing to do for Cyrus in order to get him into the Oval Office. Tom killed Vargas on Scandal because he thought he was doing what Cyrus wanted. But now he's using the situation to his advantage to dragged Cyrus through the mud and make him regret ever rejecting him in the first place. I'd say, mission accomplished.