It was not that Ye Shuang's reaction was too fast, but the incident with Cedrick's family had been brought up too often recently. For example, after Ye Shuang was led away from the real business by Edward's speech that was twisted by madness and vengeance, Ye Shuang actually made the call again, and then she found out the answer that she had originally been looking for.
To put it simply, the problem within the organization was due to some disorder created by certain people. Ye Shuang was not that surprised when she heard that. After all, she had just discovered Edward's incredibly well-hidden identity. So, if there were one or two more 'Edward's in the organization, it was honestly not something that was so hard to imagine. There could never be only a single voice within a group. Within a good or bad organization, the possibility of having a traitor was equally high. The difference was how they would feel and react after finding out about the betrayal.