If it were me, I would clean deposits off the spigots with something
like CLR or white vinegar, rather than waiting for the softened water
to do it. Once cleaned off, they will not build up again now that the
water is softened. You can soak a spigot or shower head in white
vinegar by putting the vinegar in a plastic bag and rubber-banding the
bag to the fixture so that it remains immersed in the vinegar. Then, a
little scrubbing with an old toothbrush and it should be good to go.

Jo Ann