Also, by synchronizing Mac and iPhone contacts via iCloud, birthdays registered on the iPhone can be displayed on the calendar, so please take a look at this as well.
How to sync contacts between Mac and iPhone (iCloud)
Birthday display and notification (alerts)
birthday display
Birthday notifications (alerts)
On the day (9:00 am) 1 day before (9:00 am) 2 days before (9:00 am) 1 week before
