If I have 2 notifications on the lock screen from two different apps, I used to slide one of them and it would take me right to that app. With touch ID, you can't do that. When you put your finger on the home button, it unlocks and takes you to the last app you were using, creating an extra 2 steps to get to my notification.
My code is now a 16 character phrase containing letters numbers and special characters. I won't type this instead of simply putting my finger on the home button.
It works exactly like it did in iOS6. Slide notification, unlock, go to the specific app. I think what the confusion is that there isn't a "slider" like there was in iOS6. With the flatness being the norm, the notifications just slide off screen and you are taken to the passcode screen. It's isn't completely clear that it's linking to anything. But be assured, it's the same process as before, just with no sliders in place.
In all fairness, the way it worked before seemed to make more sense, this is just a new experience.