How do I orientate the navball properly with a probe?

You could use the chase camera (pressing the change view "V" key until the right view) or the IVA view (with the "C" key), but the right way would be to learn to use the navball.

Navball Guide

and the maneuver nodes.

Maneuver Node Guide

Anyway, it really depends on what you intend with "properly".

The problem you're facing is one I fixed earlier this week.

If at some point your craft switches its alignment (e.g. putting a plane on the launcher that is NOT nose up, or building a satellite/rover upside down on top of your rocket), the game doesn't pickup on that change. It will always define the center of your nav ball as 'the part that was pointing up when you launched'.

You can fix this by either using docking ports or extra command pods/probes. If they are pointing another way than the main command pod/probe, and you click "control from here" from the right click menu, you will see your nav ball change.

In your case, I'd suggest putting a docking port on the nose of your plane. Once you've detached the plane and your direction has changed, use 'Control from here' on the docking port.

If you test it on the launch pad, you'll see that if you have your main command pod selected, the nav ball will point up (the blue center). If you use "Control from Here" on the nose docking port, the nav ball will be pointing toward the horizon on the nav ball (blue/brown separation).