From the plants in the background, it looks like you are in a warm spot. They look very healthy.
Tomatoes will grow year round in a frost free climate, but you will have more problems with fungal disease in the monsoon season Tomatoes like a soil that is rich in nutrients and slightly acidic with a pH 5.5-6.8. Alkaline conditions will lock up micronutrients and plants will be small. Wood ashes and chicken manure will make soil more alkaline as well as adding dolomite lime that is not needed. Compost should be added to help retain moisture. Most aerated composts are alkaline. Peat moss is an acidic compost.
Tomatoes are heavy feeders and need a rich soil. A soil test would be best. You need a fertilizer that has micronutrients. Be careful when mixing in your own organics. You have to pay attention to the ratios and realize what each component contributes
Peat moss - acidic compost, holds water but difficult to wet when it is dry. Good for root development and for mitigating alkaline conditions. It will lower pH faster and longer than sulfur
Sulfur- fertilizer, insect and fungicide, and lowers pH of alkaline soils (takes 6 months and you should not try to lower pH more than 1 pt at a time. You need to know pH before attempting to adjust pH up or down.
Dolomite lime- often added for calcium for tomatoes, however, also raises pH and makes soil more alkaline so it should not be added to alkaline soils or in large quantities or it will alter pH.
Chicken manure - high in calcium, one of the highest organic nitrogen. Can raise pH by a half a point as it is alkaline from the calcium.
Wood ashes - source of potassium,but is extremely alkaline so you cannot add too much or it will alter pH.
Bone meal, bat guano are primarily phosphorus. Most soils don't need a lot of phosphorus, so you should test your soil before adding
Organic nutrient NPK will vary batch to batch and will generally be very low. It also takes about 6 months to 2 years for all of the nutrients to be released as it is in a form that must be converted by soil organisms before most of the nutrients (especially nitrogen) is in an inorganic form that the plants can use. If your soil is relatively poor to start with, it will take time for the soil microbe population to build. It is why most organic gardens get their best production after 3 years. To keep production up, organics require constant inputs of organic matter.
Composts should be blended and made from a variety of sources. Homemade composts may not be hot composted so may contain weed seeds and all pathogens may not be killed so it is best not to compost any diseased plants. You need to be careful when adding things like wood ashes and dolomite lime because you can add too much. A soil test is best taken before you start amending the soil. If you ask for organic recommendations, it will tell you the quantities of manure, compost, and organic fertilizers you will need to add for nutrients and pH.
Pots with potting soil, are a relatively sterile mix and do not contain a large amount of soil microbes so it is difficult to do organics in pots unless you supplement heavily with fish emulsion, kelp meal, compost and manure teas on a weekly basis. Since you have to constantly be supplementing nutrients organic pot culture is really not sustainable and does not help the soil which is the intent of organic farming practices.
Happy gardening in Hawaii. Gardens are where people grow.