Do spouses count as fasting if they did not perform ghusl until after Fajr began, knowing that the wife performed ghusl before Dhuhr and the husband after Asr?

If the spouses continue intercourse after the dawn becomes clear, then they have intentionally broken their fast, and they must make up for that day (qada'), and the husband must offer expiation (kaffarah (definition)). However, if the husband withdraws immediately after the dawn becomes clear, then their fast is valid, and there is no qada' or kaffarah upon them, and this is the more correct view. As for delaying the ritual bath (ghusl (definition)) until after dawn and letting the prayer time expire, it is a grave sin that necessitates repentance and making up for the missed prayers.