Uptil now Ive had planes with spinners installed through screws. Recently I got the WM Giant scale mustang and it came with a spinner with a spinner nut. My question is that should the nut be used to tighten the propellor instead of the nut which came with the engine? or I should tighten the propellor with the engine nut and then just put the spinner nut over it?

It depends. If you have the room and/or you need nose weight use them both. I personally use only the adapter nut. But make sure you use both washers.
Also dont over tighten the screw that holds the spinner on. It's easy to bow out the spinner around the prop clearence slots. Later David