Read the book & saw the movie (unmissable!) & every reference (the woman & girl outside Auchwitz, for example) refers back to something (wife/daughter) in Teddy's life but 2 things puzzle me-1) the fire reference. Nowhere do you see him setting or even contemplating setting, the fire and (2) his seemingly indifference to the sons who were also killed-everything refers back to the daughter, including the name assumed by Rachel Soldano. That seems sloppy for such a consummate craftsman!
Teddy (Andrew) did not set the fire. The fire refers to the one his wife set on their home in the city. Teddy attributed that fire to Andrew because it was just one more sign he missed and blames himself for.