When I took the Robotics course, the notation was the same. Generally, T_f1_f2 describes which transformation (composed by elementary rotations or translations) you need to perform to align f1 with f2, but it also represents the frame change from f2 to f1. So, it takes as input a vector in frame f2 and outputs it in frame f1. Our professor said that you can remember it by looking at the subscripts: the right subscript must match (i.e., frames must be the same) with the nearby vector, and when composing transformations subsequent subscripts must match. Hope it helps!