I don't know how you want to classify that in your scheme. It's not factual about the past. It's not counterfactual in the present. It's conditional about reality at any time: If something happens at time t, something else might happen after time t, say t+.
"Will not have" means "my brother won't be edgy around dogs at any time in his life." But since the seeing or not of the dog attack is linked in the story, the time that the brother won't be edgy around dogs corresponds to t+, even though one could postulate that he wasn't edgy before that either.
Student or Learner