Yes, this happens. Stabilization means getting you to a place where you are not in constant crisis before digging into trauma. If you are still having angry outbursts regularly, your nervous system is too dysregulated to process trauma safely. It can retraumatize you instead of healing.
A good therapist should focus on coping skills that actually work for an autistic nervous system. Standard grounding techniques like deep breathing might not be enough. Somatic methods, like movement or temperature changes, can work better. Also, look into DBT skills. They are more concrete than talk therapy.
If your therapist admits she cannot stabilize you, ask for a referral to someone who specializes in both trauma and autism. Not all therapists are equipped for this. You are not broken. You just need the right fit.