They found out during the day that Ramadan had begun, so they fasted
Question

Some of our Muslim brothers did not know that Ramadaan had begun until after the sun had risen, but they completed their fast. Is that sufficient or do they have to repeat their fast?.
Praise be to Allah.They have done the right thing by refraining from eating etc for the rest of the day, but they have to fast another day in its stead. 
Standing Committee for Academic Research and Issuing Fatwas, 10/245 
The reason why they have to make up the fast is that they did not have the intention of fasting from the night before. The Prophet (peace and blessings of Allaah be upon him) said: “Whoever does not make the intention before dawn, there is no fast for him.” 
Narrated by Ahmad, 6/287; Abu Dawood, no. 2454; al-Tirmidhi, 730; al-Nasaa’i, 2331; classed as saheeh by al-Albaani in Saheeh Abi Dawood, 2143.