Hence the 45 minute hour of therapy?
The T is supposed to take time to refresh and regroup between clients to keep the spill-over from happening.

My new girlT will bring her prior client to the waiting room (location of the elevator) and then take me immediately. That kind of bothers me. Once I said "You are really ready for me?" and she said yes. I'll have to say something next time it happens.

BUT to your other point, she admitted one week that she'd gone to the waiting room at the appointed hour to meet with me, and I wasn't there. Then she realized, oh no! Black Canary is NEXT hour, not now! She realized it must be a new client, but no one had a clipboard with the paperwork. So she finally had to ask "Who is here to see (name of T)?"

I think it's normal to have some spill over no matter what - if things are tense at home then my work suffers, when I have a horrid meeting at work then my next meeting won't go as well, and when I have a rotten day at work I tend to go home crabby. The key is to recognize it and set it aside - most Ts are pretty good at it, but not perfect.