The bad news about mould is that it is everywhere, it has populated our planet for billions of years and is a tough survivor. The good news is that it is a really thirsty organism. Think of it like a plant, if you don’t give it water, it will die and if you keep the conditions dry, it will never return.
The kitchen cupboards are a nice dark, damp space for mould to grow and it will be feeding on the organic material of which the cupboards themselves are made. If you can improve the ventilation to this area, you will have a fighting chance of stopping it from growing as improved air flow helps to reduce humidity and condensation.
Look also for any other sources of excess moisture, for example leaking water pipes nearby. Evaporating water from puddles caused by leaking pipes create the sort of damp conditions that helps mould to thrive.
I’m not sure what types of mechanical ventilation systems are available in Australia and you need to make sure that whatever you do does not impede the performance of your air conditioning, but a good place to start would be to look up a local ventilation specialist and ask them to call round to give you some specific advise as to what measures might be available on this front.