Dear me. For a start, an executive committee member cannot be paid without approval of the owners at the AGM. So unless there was a resolution to pay the Secretary/Treasure at the AGM which was approved by the owners, the payment is illegal. This type of approval has to be done after the services have been provided.
Note the Committee does not have the power to approve such a payment.
Section 95 of the Act provides that if an audit is carried out, it must be in accordance with Australian Accounting Standards.
From the information you have provided, whatever it is that this person has provided is not an “audit”. An audit is conducted by an independent third party who is qualified to carry out the work.
I am not sure if it is illegal to hold oneself out as an auditor, but I would be telling the Committee member to hand the money back, and if you want to have an audit, get someone qualified to do it. It may also be a good idea to remove this person from their position as Secretary/Treasurer and tell the manager they must not pay any invoices or expenses without sign-off from the Committee.