Is it obligatory to make up or offer expiation for someone who broke their fast for three days in Ramadan and fed ten needy people for each day, then later doubted making up those days?

If a trustworthy person from your family informs you that you have completed your fasting obligations, there is no harm in accepting their word, and you are not required to make up the fasts. A group of scholars has adopted the view of accepting the word of a reliable person in many acts of worship. Examples include: if one doubts the number of circumambulations (tawaf) and a trustworthy person informs him, or similarly in matters of fasting and purification, the word of another is accepted.

Abu Al-Walid Al-Baji said in Al-Muntaqa: "And whoever doubts his circumambulation (tawaf) and is told by someone performing tawaf with him that he has completed his tawaf, Malik said: 'I hope there is some leniency in that'... This is because the accountable person does not refer to the words of one who is not with him in the worship during prayer, because it is an act of worship for which congregation is prescribed. As for the worship in which congregation is not prescribed, the word of one who is not with him in the worship is considered, such as purification and fasting."

If you were to make up the fasts as a precaution, it would be good. The expiation for delaying the making up of fasts is only obligatory upon one who has been negligent in delaying, and it is to feed one poor person for each day for which the making up was delayed.