I sincerely doubt that an agency expects a T to answer the emergency line when they are in session. The T's probably all schedule their sessions around their responsibilities, but sometimes there is probably an emergency with the T in the agency-- s/he is sick, or they have to leave to care for a sick kid in school, etc. Your T obviously got stuck with this responsibility when she didn't expect to, and decided it was probably better not to cancel your session and take the chance that no one would call during that hour. Obviously that didn't happen, but my guess is that she was between a rock and a hard place, and didn't intend for things to work out as they did.

However, I would have also felt unnerved by the lateness and the phone disruptions, so I get how you feel. At the same time, I'd encourage you to talk to your T about how you felt because it will help you understand that she mostly likely got stuck when she didn't expect to, and she had to make a decision that she thought would be best for you and her other responsibilities, and it turned out badly. Sometimes that happens, and learning to be okay regardless of things going wrong in session is an important skill to have.

And having this conversation will also help you understand your interpretations of what happened and how they might be skewed and distorted and unhealthy. Once one of my T's next client after me knocked on the door about halfway through the session, and T answered it and explained to him that he was early for his session (for some reason he thought he was late). It freaked the beejeezus out of me, because I happened to be talking about something related to my CSA perpetrator. When the knock on the door came, I was sure it was him-- which of course doesn't make sense because he is disabled and doesn't know I'm in therapy, much less where it is.

Since my goal is not to be triggered by innocuous occurrences, it did actually have a silver lining in that this experience (and there have been a few other disruptions during sessions for different reasons) has helped me be less reactive to nonthreatening events outside of therapy too.