Apple - Notifications on dual monitors: how can I specify which monitor?

You should be able to do this by choosing the monitor on which the menu bar is active.

Try:

• System Settings -> Displays -> Arrangement

and drag the little white bar to the monitor where you want the notifications to show up.

In the picture below, the bar is being dragged from the left to the right window.

In case you have mirrored displays and you have no notifications appearing on either screen, you might have fallen victim of the "DO NOT DISTURB - Enabled while mirrored" setting.

To change this setting, open the notification centre on the right, scroll up in the list to reveal the hidden settings panel, and toggle the DO NOT DISTURB switch.