Xterm is not special. Your mouse pointer is. Chromium will appear on the monitor your mouse pointer happens to be in. This is probably the default behaviour of your window manager.
Chromium does not respect the usual window position requests. You cannot tell Chromium where to appear, you must tell your window manager where to place the Chromium window. Methods of doing that, if they exist, totally depend on what window manager you have.
If you ssh to your machine as the user that has started the X session, you should have no problem connecting to that session.