I think it is important to note that Dally and Johnny share similar family backgrounds; both had parents who showed no true affection for them, and were even physically abusive. This is probably at least part of the reason for Dally's brotherly feelings for Johnny. In addition, Dally's concern for the possibility of Johnny becoming hardened may be founded on their similarities. Because both of them had endured numerous injuries (physical and emotional) at a young age, they were most at risk to become the sort of hardened person that Dally feels he has already become.
Johnny thinks he has "a good chance of bein' let off easy", for killing the Soc because he has no police record and the murder was in self-defense, but Dally is not so sure about that. He points out, "Us greasers get it worse than anyone else", meaning that from his experience, the court system will most likely be hard on Johnny because he is from the "wrong side of the tracks". Dally, with a tenderness uncharacteristic of him, really cares about Johnny and is worried what time in jail would do to him. He says, "I just don't want you to get hurt. You don't know what a few months in jail can do to you...you get hardened in jail. I don't want that to happen to you. Like it happened to me..." (Chapter 6).
Dally dosn't want Johnny to turn himself in because for killing people you get the electric chair. Dally didnt want Johnny to die.