I understand the App Switcher follows the Dock. Other answers here confirm as much.
However, is it possible via some hidden command-line preference to force the Application Switcher to display on the main display at all times? Whereas "main display" is the display in the System Preferences > Displays > Arrangement preference with the menu bar.
I personally have my dock hidden on my left-most display, but even switching the dock position to the bottom is a hassle since it requires first launching the dock from the desired display before switching the app switcher's location.
Best Answer
If you are OK with losing the new features of Maverick's multiple displays, open System Preferences, click Mission Control, the uncheck the box that says, "Displays have separate spaces". Log out, then log back in, the problem should be resolved.