I'm sure mine has changed. I do remember shooting the first one and being more focused on the scene rather than being elated. My first deer (a doe) was with a bow on the west coast (where I grew up) and when I hot her she let out a wail. I've never had a deer do that again, but I think for that being my first deer it took some of the elation out.
As for now, I immediately focused on where the deer is running, where I hit the deer, where it was standing, where I heard it crash, etc., so that I know how long to wait and where to start tracking. I only really get excited when I find it and then have a silent celebration in my head. I always have a moment with the deer and thank it.