Quick Story: My first house was over 80 years old with the original galvanized plumbing. I intended to live in this house for 1 year, then move into a bigger house, just a quick turn house. i installed a softener and instantly had orange, nasty water. I knew it was nothing more than the softened water "cleaning" the galvanized pipes, but I was surprised that 3 months later my bath tub would still fill up with water so dark you could not see the bottom. It did eventually clear up and all was good, but this was almost 6 months of regular use.
Do you have galvanized? Old plumbing? A softenr produces much cleaner water and it will remove the old rust, calcium, magnesium etc from the plumbing. Be patient, it will suually clear up but it may take a very long time. It will usually be the worst in the morning when the water has been sitting in the plumbing all night. After heavy use, the discoloration should lessen, but it will not go away entirely. How old is your plumbing? It may be a good time to repipe.