This is because once the Exam is created, for it to be displayed in the calendar or to send an SMS, that Exam's schedule should be published. Until and unless, the schedule is not published, the Exams schedule wont be displayed in the calendar. For publishing the exam schedule, Go to Examinations module - Exam management, Select the course and batch and the Exam. There is a link to the right of the Exam name, Publish Exam Schedule

Click on the link and the Exam schedule will be published. User will get a confirmation link as shown below

Once the schedule is published, the users in the batch can login and in their calendar, the Examination will be shown.