Fungus and mildew are problems that come from the humidity created by everything drying up after the rain. I thought it was the rain itself, but then I figured out that it could rain two weeks straight but the fungus only appears within three days of the rain stopping in the humid weather that follows.
In the summer, when it has not rained for awhile humidity levels are low and fungal problems are not as bad unless you are watering at night and you have planted too closely to provide adequate air circulation.
I inspect the plants when I water and I have a dial type pistol head. Showering the undersides of the leaves with water is not enough. It is best to use the jet setting so the bugs can be blasted off. this works with aphids, spider mites, and white flies. For mealy bugs, I have to use a scrub brush. Every day I go out to water, I check the undersides of the leaves especially of hibiscus, pepper, corn, and eggplant which are the usual targets. I also keep a zip loc bag in my pocket to bag snails, slugs and infested leaves to be sealed in and thrown in the trash. Sometimes I just cut the plants back because it is just easier to control the bugs that way.
I have not used anything more than alcohol and sulfur on my plants in the back yard for about three years now. I am not 100% pest free and never will be relying on natural controls, but I still am able to get a reasonable harvest and tolerable damage levels and I am not spending a fortune on chemicals that have to be repeatedly sprayed to control the bugs and switched out to prevent pesticide resistance. The only exception is slug bait and the snails and slugs are winning.
Sulfur BTW also kills spider mites but you need to be careful using it on very hot days because it can burn plants. I use the sulfur more to control fungal diseases and I spray within 3 days of the rain stopping.
I also have flowering plants to provide nectar, marigolds, dill, fennel, basil and other herbs to attract beneficial insects. I don't have as many bees visiting as I did a few years ago, but the bees do visit daily so I do not use neem. Unfortunately I don't have a toad or a chicken, hence I use a lot of slug bait.
Happy gardening in Hawaii. Gardens are where people grow.