How does the relationship change between Darry and pony boy when Johnny turns himself in
This question is a bit incorrect. Johnny doesn't ever actually turn himself in. He decides to turn himself in during chapter 6, but he is injured and badly burned in the church fire while helping to rescue the children. Johnny dies in the hospital before ever turning himself in.
Chapter 6 is the turning point in the relationship between Darry and Ponyboy. Prior to chapter 6, Ponyboy thinks that Darry doesn't love him very much. Darry is very hard on Pony and always criticizing him. At one point, Darry even hits Pony hard enough to send him across the room. This confirms Pony's feeling about his brother Darry, and he runs away. But in chapter 6, Pony sees Darry crying at the hospital. At that moment, Pony had a revelation about Darry's actual caring attitude toward him. Here is the text:
"In that second what Soda and Dally and Two-Bit had been trying to tell me came through. Darry did care about me, maybe as much as he cared about Soda, and because he cared he was trying too hard to make something of me. When he yelled "Pony, where have you been all this time?" he meant "Pony, you've scared me to death. Please be careful, because I couldn't stand it if anything happened to you."
Darry looked down and turned away silently. Suddenly I broke out of my daze.
"Darry!" I screamed, and the next thing I knew I had him around the waist and was squeezing the daylights out of him.
"Darry," I said, "I'm sorry..."
He was stroking my hair and I could hear the sobs racking him as he fought to keep back the tears. "Oh, Pony, I thought we'd lost you... like we did Mom and Dad..."
Later in the book it is super important to Pony to find out if he asked for Darry in his delirium. He doesn't want to hurt Darry's feelings by not having asked for him. That is a very different attitude toward Darry than Pony had at the beginning of the novel.