We can never know for certain, but I doubt he pauses to blend in after killing the president. He is making tracks until someone stops him. Not running or anything to draw suspicion, but he keeps moving. Even when his bus gets caught in traffic, he is quickly off and, on the move,
The Dallas reporter Pierce Allman, who was at the scene of the assassination, said he ran into the building shortly after the shooting to phone in his report (he said he heard three loud reports). He said he came across a young man and asked for the location of a phone. Later he said the Secret Service called him and said Oswald mentioned seeing a young man with a crew cut ask for a phone.
Allman: "I went up the steps of the depository building and there was a guy in the doorway," Allman said during that museum event. "And I ran up to him and asked him where a phone was, and he jerked his thumb and said 'in there' [while motioning over his shoulder]. I then went on in.
"About two weeks later, I had a call from the Secret Service. They finally said, 'Are you familiar with the testimony of Lee Oswald after his arrest?' I said, 'No.' They said, 'Well, he states as he was leaving the depository building, a young man with a crew cut rushed up and identified himself as a newsman and asked where a phone was. Based on what he has said and what you have said, this is you.'"
There's no other account of any of the workers who were on the steps of such an incident. Who else had a crew cut as well? Obviously Oswald could have changed his mind and gone out the back. Seems more risky; another minute and there's a chance of the building being blocked. But in all of that chaos it makes some sense he would just try to blend in and leave.
