Dauntless caught up to Feng Huai and Gong Sun as soon as the deadline was reached. The two were actually standing close to their headquarters. That's why one of the employees who was about to go home saw them and quickly took a picture of the two standing near the Imperial Academy.
It was purely coincidence that the head chief of their department was also tasked to look for Gong Sun's whereabouts once the deadline was over. He saw his junior's chat in their department's chat group and quickly headed over to where Gong Sun was seen standing. He didn't forget to bring the police that was already called for their arrest. Naturally, the arrest warrant was not forgotten.
It was just that Feng Huai should have been a complete bystander. Dauntless had only known about him recently and they were unclear of his involvement with Gong Sun. However, when he started running, Gong Sun grabbed him and told the police officers that he was an accomplice.