Sayyiduna Salamah bin al-Akwa' (may Allah be pleased with him) narrates that the Messenger of Allah (peace and blessings be upon him) sent a man from the tribe of Aslam to his people on the day of Ashura and said: "Order them to fast this day." He said: O Messenger of Allah! Tell me, what if they have already eaten? He (peace and blessings be upon him) said: "Whoever among them has eaten, let him fast the rest of the day."
Imam al-Bukhari (may Allah have mercy on him) recorded it in his Sahih, and it has been narrated in a hadith that he ordered it to be made up.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8035
Abd al-Rahman bin Maslamah (may Allah be pleased with him) narrates from his uncle that they came to the Prophet (peace and blessings be upon him) on the day of Ashura. He (peace and blessings be upon him) said: "Have you fasted this day of yours?" They said: No. He (peace and blessings be upon him) said: "Complete the fast for the rest of the day, and make it up."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8036