This is a specific school of thought that many therapists do not believe in or practice. I have never even had a conversation about attachment style in my own therapy, I just know how I am and why I am probably like this. Some Ts might try to relate and empathize with you in order to form a connection, but in my experience that's just what people who are socially oriented do. They like to relate to people. If you don't they may try to push you because they think it's somehow unhealthy, so I understand where you're coming from with that perspective. But the "right brain therapy" where the t tries to experience what you experience emotionally in order to modify attachment style is not appealing to me in he least. I find it phoney and I would not return to a therapist who acted like this. I this is at all what your T is like I now understand 100% why you ask her to stay back and not talk. I also understand now why you find the supposed empathy so strange or insincere. I would feel the same way with a T like this.

That said, I do think it's possible for the relationship with a T to alter relationships in other areas of your life, especially if it's a positive one. To go from distrustful to more trusting or socially anxious to a little more confident will indirectly affect your attachment style. I don't think this is how therapists are always approaching their therapy nor are they doing anything without your knowledge. It's just human nature and shows how much people affect each other without really knowing it.