Let we first answer you second question, why Suzuki Thailand doesn't help you with this question is probably because they have no service manual for this model on hand and the Suzuki DRZ400SM is a motorcycle that was a grey/parallel imported model (Suzuki never officially introduced it in the Thai market).
For the main question, we like to see just a splash of coolant in the overflow bottle when cold. Since Suzuki was kind enough to place the bottle on your motorcycle in a most inaccessible spot, above the swingarm pivot, topping it off requires some creativity. You could pop the hose off and fill with a syringe. How safe and boring. I cheat by using the cooling system pressure to fill the bottle. It sounds complicated, but it isn't.
Make sure your radiator is full when cold. Check the bleed screw opposite the radiator cap to be sure all the air is out. Warm up the motorcycle just until you see some coolant forced into the overflow bottle by expansion. Warm, not hot! Turn the motorcycle off. Slowly and carefully (wear protective gloves and goggles) twist the radiator cap, releasing the pressure. Leave the cap loose until cool. Top up your radiator once more and refit the radiator cap.