Place the salmon fillet in a large container skin-side down. Bury the salmon in the salt, making sure that no meat is exposed. Cover with plastic wrap and refrigerate for 24 to 48 hours. Remove the salmon and rinse well with water, being sure to remove all of the salt. Discard the skin and dice the fillet into 1/4-inch cubes. Measure out 2 cups of salmon cubes.
In a bowl, mix together the salmon, onions and tomatoes with your hands. Don't be shy; "lomi lomi" means "to massage" in Hawaiian. Refrigerate until cool, 30 minutes to 1 hour, and then serve.