Apple - How to choose on which display Application Switcher shows?
Try moving your Dock to a different screen in System Preferences > Dock > Position on screen. The Application Switcher will open on the same display as the Dock.
You can also quickly move your Dock (and Application Switcher) to another display by hovering your mouse on the very bottom of the desired display for a moment.
The Dock will then rise up and appear on the desired display. (Note: this only seems to work if the Dock's Position on Screen setting is Bottom)
Please let Apple know if you find this behaviour non ideal. Personally I would prefer either of the following behaviours:
The Application Switcher is always displayed on the monitor on which the menu bar has been placed under System Preferences → Displays → Arrangement.
The Application Switcher is displayed on the display with the active (opaque) menu bar.
cmd+tab when you mouse-over the dock. The app switcher will move to the display your mouse is on.
Found this out by accident... the obvious behaviour would seem to be that the app switcher appears on whatever display the cursor is.
Update:
As correctly mentioned in the comments, you don't actually need to cmd+tab when you mouse-over the dock, you can just mouse-over the dock on whichever display you want, from then on the Application Switcher will show on that display.
However, as the question was about showing the Application Switcher, why not do both at once?