It's ok to feel it pulling on your back. Your back is having to work to help maintain torso position as you go up. But you should also be feeling the glutes and hamstrings working, etc...
You don't really 'straighten' your back to finish the lift you use hip extension to finish it...basically it is thrusting the hips forward (think shoving the butt forward) not hyperextending the back which is an improper finish.
This is one of those things where it would be hard for me to tell you if anything feels "wrong" just based on what you are saying. You kinda have to start with as close to good form as you can. Could be your perfect and it's just your back needs to get stronger. Could be you need a very simple fix in technique. Or you may need to strengthen some things....but if you really think it just doesn't feel right I would certainly act of that. But if you went into it thinking you weren't ever supposed to feel it in your back that could play into what you are experiencing.
Check out EC's articles..links posted here by Wolf, aka Sentinel aka Anuj: