On multiple computers I was able to replicate this problem. It is the same for Desktop, Fullscreen, and Windowed mode. If I have 2 monitors connected to the same video card, no matter what I choose, it will only show up on the 1st monitor with an identical name.
For instance, in the "Display Adapter" drop down in "FULLSCREEN settings" I see this on 1 computer that has 3 monitors (2 video cards):
1. NVIDIA GeForce 8800 GTS [nvd3dum.dll]
2. NVIDIA GeForce 8600 GTS [nvd3dum.dll]
3. NVIDIA GeForce 8600 GTS [nvd3dum.dll]
the 2nd and 3rd are completely different monitors and resolutions. I can correctly choose 1. or 2. from the list and everything is fine, however if I choose #3 (the monitor I DO want the visualization on) just saving the options and opening the options back up you will see that #2 is selected. I cannot get it to go fullscreen on the 3rd Monitor.
With a laptop, the hdmi output and the lcd built in both list as the same, and thus I cannot get my laptop to put the visualization on the HDMI output in fullscreen.
The best work around so far is to simply move a window on the monitor I want to use, then maximize it...but I'm stuck with the titlebar showing.