The elemental iodine (in solution in the alcohol of the tincture) reacts with the silver that forms the image and produces silver iodide, a light sensitive halide compound. Since you're doing this in the light, the halide is immediately reexposed, and when you develop, you get the image back (and since the print was previously exposed with an image, developed, and fixed, there's only enough silver present to recreate the original image density) -- the color shift is because silver iodide produced by bleaching gives a different silver grain size from the original (typically a chloride/bromide mixture, mostly bromide in modern materials), and silver grain size controls the warmth or coolness of print tone.
It might be interesting to do the bleaching under safelight, apply a suitable clearing bath to remove excess halide, dry in darkness, and then reexpose the paper with a projected negative image, in effect blending the two images. The idodide would typically be faster than the bromide in most printing papers (though perhaps not as fast as papers that include developer in the emulsion), though it would be difficult to impossible to control contrast. You could also fully fog, develop, bleach, clear and dry to produce iodide paper without a preimpressed image (starting with RC paper, this could even be reasonably inexpensive). There'd still be no control of contrast, but it might be of interest for things like in-camera negatives, since it should be faster than common paper emulsions.
Do be aware, however, that iodide places a great load on your fixer; only rapid fixer should be used, and this 100% iodide material will greatly reduce the capacity of the fixer. Iodide is also a restrainer in developing, and a 100% iodide paper might require using a pretty strong developer one-shot to get consistent results.
