You may have just missed it, it's quick. Then it only does the green flash thing the first time you pair the battery with a charger, I believe. From then on, it does a little cycle through the lights, before settling in. Two of ours I saw it, the other I didn't, but they all work fine.
Is it charging? Are the lights on the charger cycling through and filling up to green as time goes on? If after the time described in the manuals (both battery and charger) all lights are green and the fan is off, and your tool works for the normal time, you are probably good.