The script would not turn on dual-display. If that's on when it shouldn't be, it must be the way the default lister (or layout, if you're opening a layout) is set up.
If Preferences / Launching Opus / Default Lister / Update Default Lister automatically when closing a Lister is on then the default lister should look like the last window you closed. If it's off then it should look like the last window you used Settings > Set as Default Lister in.
Preferences / Launching Opus / Startup / Open the Listers that were open when the program was last closed can also come into play when launching Opus if it is not already running.
(Also, just to clarify, "Explorer" is a style, not a layout. Styles usually only take effect when you click on them in the menus/toolbars, and only right at the moment you click on them. After clicking on a style, you can change things in the window and no longer have it matching that style, such that selecting the same style again will change things back. The old Styles tabs from Opus 9, which it sounds like you're still using, were misleading as they suggested styles were states when they aren't. That's one of the reasons the default toolbars changed to no longer use tabs and move Styles into a menu.)