I don't think the tapered bearing kits fit all the way in. Mine definitely stand out of the stem, and I have yet to see a bike that has the tapered bearings seated all the way down the way the ball bearing units do.
The races won't rotate in relation to whatever they are attached to. The only thing that rotates are the tapered cones. Please post some pics, because I have a feeling I'm misunderstanding your question.
Camelman