Here's the skinny on how extended screens work. I recently explained this to someone in an email support request - so forgive me if that happens to be you.
Assume your screen is a typical 1280x1024 size, for the sake of this example. That means your screen is 1280 pixels wide and 1024 pixels tall. The screen is a coordinate system described by (x,y) where x is the horizontal pixel number and y is the vertical pixel number. The coordinates start at the top-left with (0,0). So in this example the bottom-right corner would be (1279, 1023). This, however, isn't the entire desktop. The entire desktop is actually very big, something like 65536x65536. Your "display" is more like a "viewport" onto the entire desktop. You can only see a certain section of the entire desktop at any time - however big your physical display is (1280x1024 in this case). And it's always positioned at coordinates (0,0). If you start at (0,0) and go one left and one up, you're at (-1,-1), which is a perfectly valid desktop location. Likewise, from the bottom-right you can go right 1 and down 1 to arrive at (1280, 1024).
This is all most applications know, and definitely all the TD knows. It knows you have this giant sized desktop, that your display size is 1280x1024, and it is positioned at (0,0). If you have a second display configured to be to the right of the main display, then really you've got a second "viewport" onto the entire desktop. It's top-left coordinate would be (1280,0). But the TD has to be configured to know this - it can't detect it.
To open dialogs only on the "main" display, the TD must simply position the dialog within the center of the (0,0) to (1279, 1023) coordinates. That's all it can do.
What this means is that it is up to you to (a) configure your extended display properly within Windows, and (b) correctly explain to the TD how you've got it setup. This is unfortunate in that it would certainly be easier to have the TD figure all of this out by itself and save some people some configuration headaches, but it just doesn't have access to that sort of information.
So here's what I would do. Configure things the way they "should be". That is, configure your extended display to be to the "right" of the main screen (so if you move your mouse off of the right side of the main display it ends up on the left side of the extended display). Start the TD in window mode (Preferences -> Miscellaneous -> uncheck "Full screen mode"). That way you can use the mouse to drag the Game window like you can most other windows. Open the "Extended Display" dialog (in the TD). Note in the Game Window section at the bottom, where you move around the Game window, it also shows the Game window's current coordinates (at least where the TD thinks it is located). Move the Game window around, to the extended display and back. Use the "Move to Main Display" and "Move to Extended Display" and "Manually Move Game Window" buttons to do this, or close the Extended Display dialog and the Settings window and move it by dragging with your mouse if you need to. Note the coordinates each time. Make sure that your "main" display has coordinates starting with (0,0) in the top-left corner and your "extended" display has coordinates that would place it just to the right of the main display.
Then make sure you've configured the TD's extended display settings appropriately. Let us know what you find out.