Update 12:00 a.m. Monday: A tweet posted late Sunday on the account belonging to Eddy Cue, Apple’s senior vice president who oversees Internet services and software, said: “#AppleMusic will pay artist for streaming, even during customer’s free trial period.” An Apple spokesman confirmed that the company has changed course.

Taylor Swift announced she won't allow her latest album, "1989," to be included in the new streaming service, Apple Music, because she says Apple won't pay artists during the initial three-month...