Remove the salmon from the refrigerator 30 minutes before cooking to bring it to room temperature.
In a small bowl, stir together soy sauce, vinegar, and sugar until dissolved. Stir in half the green onions and the julienned ginger. Set the sauce aside.
Heat olive oil in a skillet over medium-high heat. Add salmon skin side down and cook until the skin is golden and crisp. The salmon will not be fully cooked through. Remove and set aside. Wipe out the pan.
Add the water, remaining green onions, and sliced ginger to the skillet. Bring to a boil, then reduce heat to a simmer and cook for 5 minutes.
Carefully slip the salmon into the pan, skin side up, making sure about ¼ inch of the filet (including the skin) stays above water.
Cover and poach for 5 minutes.
Remove the salmon with a spatula and set aside. Drain all but ¼ cup of the poaching liquid. Discard the aromatics.
Return the skillet to medium-low heat and add the vinegar-soy sauce mixture. Bring to a simmer.
Add the salmon back to the pan and begin basting with the sauce. Cook for 5 to 8 minutes, or until the fish is just opaque and reaches 125°F internally.
Transfer salmon to plates. Continue simmering the sauce 3 to 4 more minutes until thickened.
Spoon sauce around the salmon and serve immediately.