I agree that the Altra Instinct's are not minimalist. I would call them more "neutral" or "natural" shoes.
However, I disagree with the comments that you can't run fast in them. I bought a pair about 2 months ago (after finding a detailed review -
http://myemptyshoebox.com/altra-instinct-review/
). I was in the middle of marathon training, and I have gradually been increasing my speed as I have transitioned to the Instincts.
I was looking for a minimalist feel, but with enough cushioning to stand up over 20+ miles on the road. And I have wider feet, so the huge toe box is extremely comfortable.
I highly recommend them.