13:21 here. That's great OP, that you've hired someone experienced and who you trust.
I had twins and thought I'd need to overlap w/ our nanny when she started (they were not quite 4 mths old). It was apparent the first day that she didn't need me around (besides showing her where things were.) I worked part-time that first week but I think it was mostly for my piece of mind.
On occasion we've needed back-up care when our nanny is on vacation and the first time we did that I used an agency nanny who I couldn't stay home with. I had to plan to leave within an hour of her arriving - I was extremely nervous.
The woman walked in, got the basic rundown from me and then instantly took over and got the kids out of the house. The message being "I can do my job MUCH better without the parents around." It was a pretty powerful moment for me. She really knew what she was doing and it was apparent. And I wasn't helpful.
We still go through these kinds of dynamics w/ my kids and they're almost 4. Life is harder for the nanny when Mom is around. And the kids exploit that consciously and unconsciously. The hard part is getting me to accept it and get out.
