In a three car accident with one impact from the last car is that car's insurance only responsible for the damages to the back of the middle car?

If with "one impact from the last car" you mean that the rear car hit the middle car and then the middle car, as a result, hit the front car, the rear car's insurance would be responsible for all damages.

If the middle car first hit the front car and then the rear car hit the middle care, the rear car's insurance would only be responsible for the damages to the middle car.

i.e. where was the first impact?