It depends on which DVI port your display is connected.
The OS / Driver and new games work with the Primary display assigned by software through display properties. It works all the time.
Old games still recognize the first video port as primary display. It thus create conflicts.
In my dual display setups and the first DVI port is connected to HDTV. The lower DVI port is connected to the LCD monitor. My setting as primary display is the LCD monitor which is connected on the 2nd or Lower DVI port.
If you prefer your HDTV to be your primary display it is best to connect it to the 1st DVI port. Which is by hardware default is the primary display unless overidden by software setup through display properties.