It is not clear how the two months notice clause is worded. You have to show the contract to the IR Officers for them to give a proper answer. Anyway, when you are unsure, you just go according to the wording of the contract. However, although that staff of yours is not covered by the Employment Act, a section in the Act on fixed term contract may serve as a useful guidance to you.
"11. Provision as to termination of contracts.
(1) A contract of service for a specified period of time or for the performance of a specified piece of work shall, unless otherwise terminated in accordance with this Part, terminate when the period of time for which such contract was made has expired or when the piece of work specified in such contract has been completed."