Fix app window on spaces change?
This is a well documented problem with using a full screen app with multiple screens.

Essentially when you start any app into fullscreen, it starts a new desktop.  Depending on your OS and keyboard you can hit F3 (for example) to get Mission Control to show you your active desktops.

The thing you need to understand is that both screens when you use an external display display the same desktop at the same time.  You may have different windows open on each display, but the desktop layer remains the same.  When you go full screen, it falls inbetween the cracks of showing the same desktop across all available monitors, and going full screen, which by definition can only be one screen.

A lot of people would like to keep desktop 1 (for example) on one screen, and have the other screen hold a full screen app, but this would be simultaneously displaying 2 desktops at the same time, or rather 1.5 desktops...

It's an odd situation, but basically full screen and multiple monitors just doesn't work nice.

As a workaround, I would suggest using one of the many Window Management tools you can use to make your app as large as possible in a single click without actually using the full screen button that OS X provides.

I like an app called Moom for this, check out the website for various things it may be able to do to help you workaround this issue.  Many other similar apps (better, worse, cheaper or just different!) are also available.