[A8ked]

The blinking light indicated you were low on coolant, the fact it went off after a short amount of running time was likely due to the coolant in your system heating up and expanding. You added water which apparently brought the cold coolant up to an acceptable level, to where the light would not trigger when cold.

The question is where did your previous coolant go? You may want to look for leaks in your coolant system; hoses, coolant tank, water pump, tank cap.

The coolant needle just measures the coolant temperature at any given moment. It will start on the left when the motor is cold and move to the middle when the engine has warmed up.

If all you added was a couple of cups of water, you have likely not lost enough anti-freeze to make any difference.