Like all aspects of education, the question of how much supervision is needed is an individual one. Where some kids will need to be supervised continuously, others may be able to work more independently. Some students may need more encouragement to stay on-task and complete their work. Other students may do well with more independence, but still need to know that they are accountable for their work in some way. Still, other students can be highly motivated to succeed on their own and require no supervision to complete their work.
Naturally, you want to consider all the needs of the student when considering your role during his lessons. The most obvious place to start is, does the child want you to remain? They are working with an adult they most likely have never or will never meet. Are they comfortable using the computer? Do they understand how to use whatever platform is being used to teach them (i.e. interactive whiteboard, Skype)? Also keep in mind the age of your child. Very young (1st grade and below) students have different attention needs from older students which can often be helped best with adult assistance. A student with attention differences would most likely benefit from adult assistance during tutoring time as well.
Many students prefer to work 1:1 with their tutor. This format is probably the most common and works for the majority of students. As long as the student is listening to and learning from the tutor, this is a format that works. It is important to ensure, however, that your child is taking direction from the tutor and feels comfortable with him. If you can be nearby to ensure that learning is happening, particularly in the beginning stages, you can help to make sure your child's relationship with his tutor is a positive one.
Online tutoring can be a great forum for teaching your child. It can put him together with tutors and resources he wouldn't normally have access to. It can also give your child an added sense of familiarity and comfort as lessons take place in his own home. It is vital to ensure that students have the level of supervision needed in order to make online tutoring a success.