I have found from experience that birthdays are automatically entered in Birthday calendar from Contacts. But if you delete the contact - BD stays in calendar. If you import same contact again you will have duplicate birthday entries for that contact. I have managed to solve that the "ugly" way:
- deleted Birthdays calendar
- exported all my contacts to file
- reimported all contacts
- restarted the device so that Birthdays calendar is created again.
If you know what you are doing it takes 5 minutes with reboot time.