KvasdoPager is a module for VirtuaWin.
It gives you a toolbar of windows (it's like the Gnome Virtual Desktop panel applet).
You can "Drag & Drop" program windows and switch desktops using the mouse.

"Also, there's a setting in VirtuaWin that will do this. Right-click the tray icon, select 'Windows Rules'. Select each entry and look for the 'Show windows of this type on all desktops' checkbox. "
VirtuaWin has a lot of settings, but I have no idea what they do (or are supposed to do).
The setting you mention is NOT selected.