Unchecking the Birthday calendar in Outlook just hides it from view.  
To stop those notifications you’ll need to either delete the actual birthday from the calendar or edit the entry and turn off reminders. 

I think you have to toggle Agenda mail on if not already, uncheck Birthdays and then you can turn off again.

Outlook website > Gear Icon top right (Settings) > Calendar > Agenda email

I know it used to be part of MSN Alerts but was integrated into Calendar sometime around the launch of Windows 8.

yitz:

 

I think you have to toggle Agenda mail on if not already, uncheck Birthdays and then you can turn off again.

 

Outlook website > Gear Icon top right (Settings) > Calendar > Agenda email

 

I know it used to be part of MSN Alerts but was integrated into Calendar sometime around the launch of Windows 8.

 

i’ve just checked that setting and it’s already turned off and everything is greyed out

EviLClouD:

 

i’ve just checked that setting and it’s already turned off and everything is greyed out

 

What I mean is turn it on, uncheck Birthdays then turn it off again.