Hard to say without more description but one way that linux (X) handles multi-screens is making a virtual device spanning both monitors. So the graphics “screen” is something like 2400x900 pixels which might fool the settings.
When going fullscreen, yes the other monitor will be black, same thing happens on OSX. Unless of course it is a separate X-device (either virtual device or a real second card). A few years back I don’t think it was even possible to go fullscreen without actually opening a undecorated window on top of everything (so it looked like fullscreen). Don’t know what LWJGL does on Linux to make fullscreen happen so can’t say for sure. Maybe JOGL performs better.