Your memory serves you well, Don Cardi. Thats exactly how it happened in the book.

Kay had become a teacher after getting her degree, and after awhile she stopped calling the Corleone compound inquiring about Michael. Six months after Mike returned from Sicily, and after Kay's school year was done, she took a train ride down to New York to go shopping. On a whim she called the compound, and Carmella told her to come out to the compound because Michael was back in the country. She did, and the rest is history.

This is another example of how the book and the movie is different.