Why do Chauvelin's soldiers not reach the hut earlier? Do they think the Scarlet Pimpernel has escaped with the others? Why?

Percy, who is the Scarlet Pimpernel in disguise, is the main protagonist of the story. He raids the various barricades in France so as to save different aristocrats from being killed. It is for this reason that Chauvelin, the main villain in the novel, hunts him down. In his pursuit of Scarlet Pimpernel into Pere Blanchard's hut, Chauvelin orders his soldiers to stand guard outside and wait for Percy before they can do anything to the fugitives. However, by the time Chauvelin’s men get into the hut, the fugitives are already gone. The soldiers could not have reached the hut earlier, because they had been traveling with Percy, who was disguised as a Jew and had orchestrated the entire plot. He made sure that, by the time the soldiers could get into the hut, the fugitives wouldn't be there. Further, the soldiers are derailed from reaching the hut earlier by their master’s orders to stand guard and wait for Percy before doing anything to the fugitives, who are supposedly in the hut. However, by the time they storm into the hut, the fugitives are already gone. At first, the soldiers think Scarlet Pimpernel has escaped with the rest of the fugitives, but Chauvelin realizes that he had heard Percy’s singing, which means that he would be in the vicinity. His thought is further articulated by a letter left behind by the fugitives, giving them the go-ahead to leave without Percy, as he would meet them at a creek near Chat Gris.