"Register" in printers' slang is the correct juxtaposition of the different colour dots so that the final result is as desired. If the blue/cyan doesn't get to the right position with respect to yellow, for example, you will not get the correct final colour (= dark blue if they should overlap, yellow and blue details if they are to remain separate).
A registro= in register, fuori registro= out of register.
The colour separation leads to the production of separate printing "plates" for each elementary colour, so it has no sense to talk about register in connection with colour separation, but only when the ink is applied (separately for each colour) on the substrate, e.g. paper.