The best book on trauma that helped me was Judith Herman's Trauma and Recovery. She doesn't just stay with symptoms, but she describes a clear path to healing. I have used it regardless of what is going on in therapy.

The first step is to establish safety, mostly in the psychological sense. You can't jump into remembering and subsequent reactions (rage or mourning) until you have that safety in place. And to me it sounds like you are uncertain enough about your therapist that safety hasn't been completely established. I don't know the "technique" you are referring to, but some feel that "exposure" is one treatment for trauma. However, recent studies have shown that there has to be a period of establishing a relationship (therapeutic alliance) before anything else. I can't tell, but maybe your therapist is trying to allow that to happen by talking more than usual. If you can, why don't you just ask? Focussing on the relationship is an important part of therapy and has been shown in studies to have a curative effect on its own.

In terms of recollection of the trauma, people sometimes think that there is something magical that happens if you just tell the story. While it is crucial to recovery to be able to put together a coherent narrative, often people are distanced from the story (dissociated) so they can tell the story in detail, but they are unable because of the effects of trauma to connect feelings and reality to what they are saying. That's often why there is a delay in going into the details, sometimes by the therapist who wants to make sure that this stage is actually productive of healing, and sometimes by the client who is highly ambivalent about wanting to go into the story completely. Remember both avoidance and intrusion of the trauma are symptoms of PTSD.