Blackburn Exercises were used in my physical therapy for mild rotator cuff tears of my supraspinatus. There was no operation. A physical therapist evaluated my shoulder posture and selected some of the Blackburn Exercises to correct my scapula issues. I continued them for a year or two beyond my recovery as they are a conditioning exercise for scapula positioning. I do them occasionally now. He said to use high reps and light weights, 2 or 3 lb dumbbells at most, and aim for the form and to build endurance. My opinion was that the exercises worked on the middle traps and the rhomboids lying under the traps and probably other muscles. I believe that tightening and pulling the shoulder blades together and holding for a delay, of say, 6 seconds, is important to the effectiveness of the Blackburn Exercises.
I do other very similar shoulder exercises such as bent over dumbbell raises using heavier dumbbells but I personally don't consider those to be for scapula conditioning and positioning but for rear deltoid strengthening. Two different exercises aimed at two different muscle groups.
For comparison, heavier dumbbell exercise for posterior deltoid strengthening, NOT BLACKBURN -
Here is a site that describes an overall shoulder recovery scenario.
Another report describing the overall diagnosis to treatment of some shoulder injuries.
It is a mistake and risky to assume that treatments apply to any undiagnosed injury that you have.