Welcome to italk!
There is no requirement for separate accounts, however here are a few thoughts:
Separate accounts - Some teachers provide detailed feedback in the lesson comments. So separate italki accounts would separate your feedback from the child's feedback. Some teachers provide feedback in Skype (I do because this I can "continue" the previous lesson based on the notes). Of course, separate Skype accounts would help in this situation.
Shared account - The italki credits are common for you and your child. The problem of "not enough money" in this account and "enough money" in the other account can't happen.