For me, intervention is a very directive, action-oriented word. At first, I didn't see how it would apply in the sort of therapy session you're talking about (I understand its specific meaning in an addictions setting). But then, it started to feel like the exactly right word: I suspect she's reacting to your self-structure which can seem rather impermeable and self-sustaining. If "normalizing" holds no helpful meaning for you, and therapeutic expertise, if it exists at all, isn't applicable for you, and you're not seeking nor accepting of any emotional connection to her, then she may very well think in terms of "intervention." What is her means of access to your psychology (as that's how she would view her professional purpose)? She is effectively neutralized. Her reaction to that probably is to feel a need to "intervene" (or "meddle" ) I would think that if that's not what you want from her, it would be very aggravating.

Most Ts work on multiple levels simultaneously: part education, part counterweight, part ego support, part wound tending, part analysis, etc. Processing I think of as the cycling through of whatever interaction is happening, sometimes consecutively, sometimes concurrently. Sometimes the focus of such recycling is a feeling, sometimes it's a situation, a behavior, a decision--could be almost anything. Depending upon the orientation of the T, processing might occur by seeing outside issues, patterns, feelings as they are reflected in the T/client relationship in the room. And then whatever happens within the session can continue independently by both T and client--to be brought back into the session again.

I've never thought of modeling as something a T says particularly, though changes in attitudes can be revealed through modeling different language--like characterizing emotions in more humane language, for instance. Or if a client talks of abuse as "discipline" as a way of minimizing/denial, the T may provoke the emotion by calling it "abuse." I usually think of most modeling as a function of relationship. When we grow up in dysfunctional relationships, we adopt a pattern of responses that is skewed; a functional relationship with a T can model healthier responses, boundaries, expectations, etc.