Why was Louis Roulet seemingly surprised at what "DJ" Corliss testified?

Question

In The Lincoln Lawyer, the state prosecutor (Ted Minton) puts a prison cell snitch ("DJ" Corliss) on the witness stand to testify about what the main antagonist (Louis Roulet) allegedly told him when they were in a lockup:

The main protagonist — the "Lincoln" lawyer (Mickey Haller) had actually asked Corliss (through Gloria, one of his clients, who was serving time at a drug rehab with Corliss) to cooperate with Minton:

Haller apparently did that to kill 2 birds with one stone:

1. To win the current case against Roulet (his client) — charge of assault of Regina Campo — by showing that Corliss actually lied in the past about his cellmates; and
2. To get Roulet charged for killing Donna Rentiera — about which Roulet himself had confessed to Haller (talking advantage of the client-attorney privilege). Haller wanted this because the murder of Rentiera was his old case in which an innocent man got life in jail (Jesus Martinez) — in whose innocence Haller did not believe back then.

Roulet now claims that Haller had actually set Corliss up to testify about Roulet's murder of Rentiera, to which Haller reasonably responds "How?".

He questions Haller: "I wanna know how Corliss got that shit he's saying":

That questioning does not make any sense to me. Roulet must have told Corliss about it himself in the lockup. If he did not, how else could Corliss know the details?

It would be understandable if Haller had actually secretly talked to Corliss and gave him the details of Rentiera's murder. But I do not see any indication that this happens.

So, does Corliss lie or not about Roulet's bragging? If not, why does Roulet question Haller how Corliss knows about it?

Answer 1

As explained in the Wikipedia page you linked in your question:

He then sets up a known prison informant with information on the previous murder.

The "he" refers to Mickey Haller. Haller had Gloria pass the necessary info to Dwayne Jeffrey "DJ" Corliss. Corliss likely doesn't even know Haller did this; he was merely using an opportunity to reduce his sentence (which he has done before).

According to this Fandom page:

Corliss made a practice of testifying, often falsely, against other inmates by claiming that they had confessed to him, in order to get special consideration by prosecutors for his own offenses. He would say just about anything he was asked to say in order to get a lighter sentence.

That page also clarifies:

On 5 March 2005, Corliss was arrested in Los Angeles for stealing a bike. At his first appearance in court he was placed in a holding cell with Louis Roulet. Although he had no conversations with Roulet, Corliss contacted the D.A.'s office to say that Roulet had confessed to him. The prosecutor in the Roulet case thought he might want to use Corliss as a witness, but he did not want to disclose this witness to the defense. Corliss was placed in a lockup Rehab unit at County-USC Medical Center where he would be available to the prosecution but not accessible to the defense.

While in lockup, Corliss was approached by another inmate, Gloria Dayton, who somehow persuaded Corliss to add certain details to his testimony if he was called as a witness. Dayton did this at the request of her attorney. Specifically, she asked Corliss to state that Roulet had admitted killing a girl that worked in a "snake pit."

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Note that the book the movie is based on gives a bit more background on how Haller planned to get the necessary information to Corliss via Gloria:

I also thought about Corliss being in a lockdown program at County-USC. Levin was wrong and so was Minton if he was thinking I couldn’t reach his witness in lockdown. By coincidence, my client Gloria Dayton had been placed in a lockdown program at County-USC after she snitched off her drug-dealing client. While there were a number of such programs at County, it was likely that she shared group therapy sessions or even mealtime with Corliss. I might not be able to get directly to Corliss but as Dayton’s attorney I could get to her, and she in turn could get a message to Corliss.

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Louis Ross Roulet suspects Haller set this up because he obviously didn't tell Corliss, but he doesn't know how. He doesn't know that Haller managed to contact Corliss, despite Corliss's testimony seemingly coming out of the blue at this late stage.