That’s completely at your discretion. Some parents have things they want to get on with, others would rather be present especially during the first lesson.
Because the lesson takes place in your home it will depend where the tutor and the child are working. Sometimes a lesson takes place at a kitchen table and if it coincides with you preparing a meal, you will inevitably be around.
The choice is yours.
One family I went to many years back used to use me as a babysitter. She would leave for London as I knocked on the door leaving me responsible for both children. The official babysitter would arrive as I left.
To be honest, I don’t think it is fair if I ask my tutors to be babysitters for people. If you are leaving an older child alone at home with the tutor, just advise the tutor in advance that you won’t be there and I’m sure something can be arranged.