Sounds like the officer was being pretty nit-picky.
Technically the law says you have to tag the deer immediately. But, since you haven't attempted to recover the deer yet, how can you tag them? You can't tag them until you recover them.
When I shoot a deer on my place I typically let it lay. I go back to camp and get out of my heavy hunting cloths. I then put on my light weight waders(my place is primarily swamp), get my Jet Sled Jr plastic sled that I use for dragging deer, and then I go out and recover my deer. Then when I get to the deer the first thing I do is tag it. But, for the 45 minutes to an hour it is laying out there it does not have a tag on it.
One other thing. I don't know why it is any of this officer's business how much shooting you do if you are on private property. If I want to walk around my woods and shoot at trees, that is not the DNR's business.