Yes, the Oz rules apply and the Australian authorisation also says "essential flight crew only". Any student pilot is not an essential flight crew. Also check with CASA but under special flying permit, one may not be allowed to conduct flight training.
OK, I've found one very good reason why the student is not permitted to fly. The Oz Civil Aviation Act 20AB states that any unqualified person must not fly the aircraft Penalty - Imprisonment for 2 years.
By implication the Instructor as PIC is "aiding and abetting" a criminal act for permitting the offence to occur.
Getting very serious indeed!