For birthday reminder popups for contacts, i personally just add them directly “as a calendar event recurring each year” on whatever day it is. Simple and works.
Apart from that if you have a eg: Google Calendar, you can “enable contact birthdays to automatically show in your calendar online via your browser” which in turn will then reflect in eM Client. So once enabled online, close and reopen eM Client and then go to the Calendar section and you will see the birthdays appear. You can then “dbl-click the birthdays that appear” in eM Client calendar to add the automatic popup reminder. Other different cloud calendars might also have that same option.