That did not happen. There isn't a single instance of Leon saying, "Everyone search the house." in any fashion specifically. The closest you can get is this: [b][i]"Look I have my orders ready, and set. Once we're all sure we're not about to be ambushed we'll make our way down to the city of Fuyuki itself. Its probably where we'll find the servants, or some sort of activity."[/i][/b]

Which is NOT an explicit order to do anything, but be alert.

The only person to do anything was Conner, sending Fran to scout; which, Scarlett took issue with, because they were better options than a Berserker to fill that role - to which, Celtchar also had an issue with, and suggest that he go scouting ahead, and Scarlett agreed to go with her Servant as his support.

Leon said, [b][i]"Lancer since you offered do you want to take point while Saber takes the rear?"[/i][/b] and Scarlett left as soon as he said it, because Conner tried to get on her for not listening to him, when she made it clear that she thought his action was impulsive and lacking the forethought of what his Servant is and does.

The only thing Scarlett felt in her collab is a complete and utter distrust in her team from top to bottom, and that she will die, if she has to rely on them to keep her alive.