Apple - cmd-tab behavior on Mavericks with multiple displays

I believe this coincides with the Dock's location. Just tested it on my MacBook Air, connected to a non-Apple external display, and whenever I moved the Dock from screen to screen the Application Switcher would follow.

You can summon the Dock on your big display by dragging the cursor to the bottom of it's display, essentially dragging down at the bottom. After a second the Dock should pop up. Once the Dock is on the desired display press commandtab to summon the Application Switcher.

Maverick has this "Displays have separate Spaces" switch in the Mission Control settings.

In my experience, if it's enabled, then the alt-tab menu gets displayed on the display that used the dock for the last time. IE, if you clicked on the dock bar on the 2nd display, next time you do an alt-tab, the menu is going to show up there.

If you disable the "Displays have separate Spaces" options, you fix this annoying thing, but you get the old full screen support that Mountain Lion had, where the full screen app in one display, disables every other display.

So far, the best way to accomplish this for people who prefer the dock on the side is to change the dock position to be at the side furthest from your MacBook.

This is done by right-clicking on the dock, choosing "Position on Screen" (if you do not see this option, try right-clicking lower down on the dock) and either choosing left or right - whichever is furthest from your Macbook.

For clarity and user-friendliness, this was extracted and augmented from Mr Rabbit's comments above.