How to stop display turn on and consuming battery power, when using Headphones remote control or volume button?
I believe it depends upon the music player app. Have you tried using another music player?

In my case, I didn't encounter this issue. I have used Samsung Galaxy 3 with several music players including stock player and also with a Bluetooth headset.

I think the app itself is the cause for this, which is causing screen wake-up on next/previous, and in my opinion is a poor implementation.

I don't know of any apps which allow to change the screen on behavior like this. It may be available in Cyanogen-mod perhaps.