If you explicitly have immunity for all things you reveal in the course of the questioning (and that immunity applies to the crimes revealed, not just that part

If you explicitly have immunity for all things you reveal in the course of the questioning (and that immunity applies to the crimes revealed, not just that particular testimony), then I don’t see why you wouldn’t reveal everything you can, whether asked or not. Any way you could possibly shoehorn “I murdered a guy in 2012” into an answer, you should, if that were how the immunity worked.