Indeed jura - it has confused me too!!! 
It is hard to describe what sort of relationship I would like with the new carer - and it is worth me giving that serious thought - before Saturday!
We do not live in a mansion, so the carer is very much on top of us, and we on top of her. We have only the one spare bedroom, and that is where she sleeps, and I share the bathroom with her. We also have only one reception room - a long lounge/diner, so if the carer wants to be somewhere other than her bedroom (which is an entirely reasonable want) this is the only space other than the garden.
It is a strange situation to be in and one that seems to vary depending on the personality of the carer. She is a stranger in my house; and I am as stranger to her.
I think there is a need to strike some sort of balance between being friendly and being businesslike; and this is not something I have previously had to do in my own home.
It is an anomalous situation as usually a live-in carer is in the house with just the client; and if there is a couple, then she is carer to them both. It is hard for the carer to adapt to that. Normally they would be "in control" of the house routines like cooking etc. in their role as carer, but with me here it is not possible for that to be the situation - she has to fit round me and how I do things.
Things have gone OK with all 3 carers in their own different ways - some easier than others. And I recognise that it is not easy for the carer. I cannot ignore the carer when they come into the room, even if I am busy with something else.
One ting that none of the carers has grasped easily is that when I am watching the proms it is not as background music!!!