The roar of an animal represents the real ability

No matter what kind of animal it is, it will usually send out a powerful roar to intimidate the opponent before fighting. The energy - lethality - of the opponent can often be judged by its roar. The energy expressed by the tiger's roar is the deterrent force. There is no need to say more here.
Dogs and other animals will definitely feel the powerful lethality from the tiger's roar, so... dogs that don't run are dead dogs with deaf ears.

Why do dogs run away when they hear it?

The ancestors of dogs are probably bred from wolves. Both belong to the canine category: so dogs and wolves are closely related.
As for running away after hearing the roar of a tiger, they may be naturally afraid of tigers because they cannot defeat tigers.
We all know that dogs’ poop-eating instinct comes from their wolf ancestors. The reason why wolves eat poop is to remove the smell and traces they leave, so as not to be discovered by their natural enemies or beasts belonging to regional overlords, which will lead to the hunting of them and their young. Big cats such as tigers are also local overlords and the natural enemies of wolves. They don't bury feces and urine.
On the contrary, they use feces and urine everywhere to mark their territory and declare their sovereignty. Once a wolf enters a tiger's territory, it immediately smells the tiger's scent and becomes cautious and fearful, fearing that the tiger will find it and be killed. Once you hear the tiger's cry, you realize that the tiger is right next to you and is in danger. It would be weird if you don't run away!
Seeking advantages and avoiding disadvantages is an animal instinct (the same is true for humans) to avoid strong enemies and strive to preserve the continuation of the family. The wolves and dogs of the ancestors passed on their experiences and lessons to the next generation, and this is passed down from generation to generation to this day. As soon as the wolves and dogs heard the tiger's roar, they formed a conditioned reflex and instinctively avoided it!