It may be the day they died (became a saint) or it can be almost any day. There is no firm rule.
The feast day of a saint can be any random date or it may fall on the commemoration day of some event of the saint's life, such as their date of death, the day of their canonization or other such event.
His feast day is September 28. He became a saint because he died the death of a martyr while working in the service of Our Lord.
Pope Benedict I is not a saint and has no feast day.
Saint Maria Goretti's Feast Day is July 6th.
The feast day of saint Mark is April 25.
Saint Christopher's feast day is July 25th.
Saint Laura's Feast Day is October the 19th.
Saint Helena's feast day is August 18.
July 24 is the feast day of Saint Charbel.
August 11 is the feast day of Saint Philomena.
November 22 is the feast day of Saint Cecilia.
The 23rd of April is the feast day of Saint George.