I don't fully understand your question but here's my answer on what i think you want to achieve. Make sure you have your display connected when doing the following.

1. Open the application you want to assign.
2. Control+Click(Right click) on the dock icon
3. You should see that a menu pops up and hover over Options
4. You'll see something that says Assign To and then some options
5. Select the display you want
6. You should be done :)

I don't fully understand your question but here's my answer on what i think you want to achieve. Make sure you have your display connected when doing the following.

1. Open the application you want to assign.
2. Control+Click(Right click) on the dock icon
3. You should see that a menu pops up and hover over Options
4. You'll see something that says Assign To and then some options
5. Select the display you want
6. You should be done :)