I believe the dog that the Romans left in Germany was a mastiff type dog similar to the Rottie. You are right in that the farmers of Rottweil then put this dog to work. Quoting from an article by Kathy Salzberg, "Most Rottie historians agree that today's Rottie is a descendant of the German working dogs, which was freely bred to sporting dogs, herding dogs, terriers and bulldogs. This resulted in a mix of traits extremely useful to farming communities that are still present in the modern Rottie."
So it seems that the Romans had the ancestor of the modern day Rottie, but the Germans engineered him into what he is today.
