Klein pretended not to notice the real dream. As he tried to stop his projection of the Death Consul, he tried to summon another version of "himself" from the Historical Void to fool the guards of the Tudor ruins, allowing his body to escape the dream and sneak into the secret mausoleum to achieve his goal of destroying it.
At the moment, he could only maintain three Historical Void projections. Death Consul Azik Eggers was one, his self-projection in a concealed state was another. He couldn't be certain if the leader of the ascetics, Arianna, was considered one. However, to be safe, he had to disperse one of them before he made another summoning attempt.
