Credence didn't run from the mob because he mistakenly thought the flappers running up to him were coming to form a chorus line. When the crowd got to him, they grabbed him and hoisted him up into the air.
"BETTER DEAD THAN RED! BETTER DEAD THAN RED!" they chanted. However, Credence didn't understand what they were saying and thought he was being crowd surfed.
"Stop!" said Newt, getting in front of the mob. "In the name of King George V, surrender that man to me!"
"And who are you?" asked the man with the monocle.
"I'm from the government," said Newt, holding up psychic paper like in Doctor Who. "This man is a Soviet agent wanted for subversive activities against the Crown. We're sending him to Wormwood Scrubs." It turns out Newt knew all about Muggle politics because it's useful for the plot in this scene. This is canon now.
"Well, I can't say that I'm surprised," said the monocle man as Credence was returned to the ground. "By the way, while you're rounding up reds, could you take care of Ramsay MacDonald next?"
"I'll see what I can do," Newt replied, as he took Credence by the hand.
"No, don't take me away from my fans!" protested Credence as he was pulled out the door. "Oh well, what's Wormwood Scrubs? Is that a jazz club?"