Isfar means that some daylight has become discernible after the true dawn. It does not mean waiting until sunrise.
أَسْفِرُوا بِالْفَجْرِ فَإِنَّهُ أَعْظَمُ لِلْأَجْرِ
Translation: Perform Fajr when dawn is more apparent, for that is greater in reward.
Hanafi jurists cite this narration for the preference of isfar. Other jurists prefer reports describing an earlier Fajr performance. The dispute concerns the preferred portion of valid time, not when the time begins.