Not necessarily. While it is normal to make a feast day the day of the year when a person is "reborn" into heaven, it is not a requirement. This is especially true with many of the ancient saints where no records remain of the date the person died. The feast day can be set for any day of the year.
The feast day of the saint is the same as the saint's day. For example, the Feast of St. Patrick is also known as St. Patrick's Day - March 17.
Philip shares the day with Saint James the Lesser.
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.
Saint Christopher's feast day is July 25th.
Saint Laura's Feast Day is October the 19th.
The 23rd of April is the feast day of Saint George.
Saint Helena's feast day is August 18.
The feast day of saint Mark is April 25.
July 24 is the feast day of Saint Charbel.
November 22 is the feast day of Saint Cecilia.