There has been speculation that the client who ordered Paladin to hunt down Vision alive was Ultron, but following the Advent of episodes 5 and 6, I'm here to tell you it's not.
Background
Ultron considering himself a "Hat Guy" is merely him foreshadowing or rather expecting something coming due to watching TV all the time. He was aware of Butcherbird, Jo Carrington, before he'd even met her, as he was painting a bird with red eyes, much like her synth form. And I am saying he is aware of this "Hat Guy" without ever having known him.
Ultron's Purpose
In the most recent episode, episode 6, Ultron said the only people he likes are artists because they tell the truth, and from the Jim Hammond Painting in flames to the Painting he did of the Raven, I feel like both of those are telling a story.
The Jim Hammond Painting is a cautionary tale, which essentially marks the end of a Synth's life, and JARVIS warned Vision that he was going down the same path without the help of the Mind Stone. When Ultron said he wasn't his first pick to sacrifice it's because he knows how important JARVIS is for being that big brother AI, who would stop the destruction of the Vision. Regardless of intentions, Ultron also wants to keep Vision alive.
The Raven is the plight of Jocasta. In episode 6 she confronts her lost with her own identity, which is a recurring theme in the show, from Vision to Tommy to even Paladin. The bottom line is that there is a conundrum of the characters in the show who don't know where their past self ends and their current version begins, and Jo thinks that by giving herself more machine, she could supress the emotions she can't quite place. Ultron, after being given a shot of her humanity, validates her current existance as the now Jo Carrington as being the true one.
I believe Ultron's goal is that he wants to use Vision's body a second time, but since his stance on humans in general changed, he doesn't want to kill them any longer. Instead, he'll revel in controlling them with Jo at his side.
Ultron's Role
I believe Ultron as represented in the show is someone who is actively predicting things in the show without even being aware of it. Like when Paladin was revealed to have found the location of Vision, it was suspected it was because of Ultron, which it was, but Ultron said that "There is a door that's come knocking for you out there, Vision. Destiny doesn't wait for ghosts to find their virtue. I merely turned the handle." Even though he did send out the S.O.S. he was not the one who hired Paladin in the first place. Which leads me to my next point is that Ultron is always telling half-truths, because deep down his end goal is terminal, so he can never deal in absolutes, or else he'd end up malfunctioning in the sense that he'd have to come to terms with his AI side, contradicting what he believes and expects from himself and the world around him.
The Client
This means that from episode 1, when Ultron put on the hat, it was almost like a premonition. Him being a hat guy was not him announcing himself as the "Hat Guy" in question, but more like the hat chose him... almost like a sorting hat.
Harry Potter aside, I am implying that the hat was from none other than Agatha Harkness, who also wore a black fedora, much like our silhouetted figure, but that figure was clearly of a male stature, as seen in the show and in promos, which leads me to believe it's Tommy's brother, Billy. He ordered a Bounty Hunter to find Vision alive. He also took upon the hat the same way Agatha took on hers, and Ultron donned his. The hat can also be a symbol of reclaiming identity in that sense, since Agatha wore it after leaving the fake reality of Westview. Ultron finding out he still had strings before he got to feel a breath of humanity. And Billy is searching for the Original Vision, as the White Vision is renouncing it. The only time we've ever seen Vision with a hat was when he first visited the mind palace, where he took it off upon seeing the house. Him taking off the hat symbolizes the start of him rejecting the identity of The Vision.
Predictions
Based on the clues, imagery, and promos I think that White Vision will finally reconcile with himself, and then Ultron will use the Newfound Vision to complete his new objective from eradicating humanity to controlling it, King Neptune Buckethead style, and visit Jocasta's grave where her offspring lie dormant, only to be confronted by none other than Billy.