If like me you have the CV on the second monitor and you save the project with that setup it should open that way.
The project should remember where all open views are. In fact if I close a view then save that project when I open the project and then open the closed view it will open on the monitor I closed it from.
However the original screen set will override what the project should remember and use the screenset's memory. I believe the behavior you describe would be consistent with a locked screenset.
From page 1302 of the manual.
To prevent the current screenset from being modified1. Make sure the Screenset module is visible in the Control Bar.
2. Click the Screenset menu and select Lock/Unlock Current Screenset.
A padlock icon appears next to the screenset name in the Screenset menu to indicate that the screenset is
locked. To unlock the screenset, select the Lock/Unlock Current Screenset command again.