Are you sure you do not have your home button set to open to turn on the iPod when double tapped? I've never heard of this behavior you speed of. Do a reset and see if you can do it again... Just by plugging in your headphones should not do anything...
I don't know about plugging and unplugging your headphones. That shouldn't be a problem. I was having a huge problem where if I was running an application that involved audio (like YouTube), my phone kept reverting back to the iPod. I did a complete restore and haven't had that problem again. Yet.
I've had it happen....both ways. While playing music and you unplug the 'phones, the music will pause.
What I see is happening when the music starts during headphone insertion, is that the ipod application is still open in the background but not playing music. (like when you are playing music but have ipod minimized while you surf Safari, then you remove your plugs during playback and the music pauses). then you re-insert your headphones some time later and the music starts again.
Just re-reading my post, and if I guess if I didn't make myself clear. I think the deal is a feature not a bug.
I was under the impression it did this for the OP regardless if something was playing or not originally. Which would be a bug in my opinion. But I do understand what you are saying and that would not be, you are correct.