I think what you experienced is simply a case of eating by accident. You eat because you thought that the Fajr adzan wasn't recited yet. In this case, your fast is still valid as long as you stopped eating the moment you noticed the adzan being recited. This is assuming that you rely on the Fajr adzan to determine the time to start fasting.
On a side note, I have experienced something that Muslim usually called "false dawn or true dawn" in Australia. There are opinions stating that the Fajr prayer time is not really correct so that we should wait around 10-20 minutes before performing Fajr prayer. In my case, in terms of fasting, I prefer to stop eating and drinking based on the Fajr prayer time just to be safe. However, in terms of performing the Fajr prayer itself, I'd still wait around the amount of time suggested above.