hmmm, depends how you fingerprinted the press I think. Input profile for your file and output profile for your device? You should use the same input profile you used for fingerprinting the press and then the output profile for the desired result. I like to embed colour profiles on images. certain profiles for colour and certain profiles for black & white images to your preference, Then on the printer you can use embedded profiles, I find on a Fiery this works really well. Hope this helps.
For offset, I have seen input profiles used for output. not a good idea. We tend to use no profile for cTp when finger printing. Some jobs have many profiles, we strip them out.