Q: Having app show on display?

We just recently got the Thunderbolt display. We have it working, made the display be the main screen in prefs. However if we open a window to watch, like Youtube video, on the display, it tends to disappear when something else done on the computer, or if another app opened. It does not quit Safari, just no a visible window, has moved out of sight. There must be a way for the window on the display to stay, isn't there? Any suggestions welcome.

— Richard