When Pope Gregory XIII proposed the calendar change in 1582, he decreed that the day after October 4 would be October 15. The change at the time was only 10 days. St. Teresa of Avila died on the night of Oct. 4/15, 1582. Her feast day is Oct. 15 (Oct. 4 was already that of a major saint—Francis of Assisi). England waited until 1752 because it wasn’t going to follow a decree from the pope. Many Protestant countries also delayed but not as long as England did.
At the time that St. Teresa died, the day began at sunset, and since she was alive at the time of sunset on October 4th, the date of her death should be October 15th.