In a small saucepan, heat soy sauce, rice vinegar, brown sugar, ginger, and garlic to a boil. Reduce to a simmer until thickened, about 5-6 minutes. Set aside to cool.
Add salmon to a food processor. Pulse until ground. Remove blade and add in ¼ cup of teriyaki sauce, green onions, panko, and 2 tablespoons pineapple juice from can. Mix just until combined. Form into 4 patties, if you have time, chill for 10 minutes. (This step isn’t necessary, it just helps the patties to stay compact.)