There are two types of app in OS X.
Document-based apps can have multiple windows, and they only close the window when you click the close button (red cross). The other type of app has only one window; and when you click the close button it quits the app.
Cmd+tab in OS X doesn't behave in the way you are trying to use it; it is simply for switching between open apps in a similar way to alt+tab on Windows (but not identical). It doesn't open apps that have been closed.
It's not the answer you want to hear, but I'm afraid there isn't a way to override the close button globally; it is a part of OS X's AppKit and can't easily be overridden by third-party software.
An easier fix would be not to click close when you only want to hide an app. Try pressing Cmd+H instead, or perhaps minimising the window by clicking the yellow button instead of the red one.