When a client adds a comment, uploads a file, or marks a client task as complete, the team member who sent them the client task and the assignee of the work item the client tasks are a part of will both be notified (if they are different people).
Anyone who adds comment or is mentioned in a comment will also be added to receive notifications. Anyone with access to the work item that the client task is part of will have the option to opt in or opt-out of receiving notifications.