Ugh, one of the reasons I switched to Linux. Windows is TERRIBLE at handling multi monitors. Basically each app has it's own way of determining where it opens, but normally it will usually open where it was last closed. What's messed though is sometimes it will mess up and you have to "train" it to open to the right screen. It's a pain in the butt. Each app is different in how it is trained. For example with Firefox you have to make sure it is not maximized, then go to file,close. But as soon as you decide to close it on the wrong screen, all hell will break loose, then you have to retrain it on the right screen again. Pain in the ass. And if you move/remove/add monitors then its even worse. Stuff will open and not be accessible.
In Linux it's awesome, stuff always opens on the screen you are currently working on, which makes the most sense. If you have an icon on your desktop on the second monitor and you double click it, it opens on that monitor, you can move the app to any monitor, and open another window from that app (ex: email client, and you open an email) and it will open on the current monitor, not the other one. Don't know why MS can't do this.