If your tap water is groundwater, it will contain a lot of metals that will start rusting if reacting with O2 and Cl (your salt). The reaction causes the brown particles (rust/ Ferric Oxide). The only way to prevent this is to filter the water continuously. This reaction is also common with salt-electrolyzed pools. Here is a forum thread that has exactly the same issue you have.
This was the answer:
That looks like rust, Ferric Oxide, exactly!
However, the cell should be Titanium, it contains no iron, but that doesn't mean it can't oxidize. Or "Rust", all metals do, Ti's oxidation would be white and powdery.
So either there is a non Ti component inside that cell that contains iron, such as steel that is breaking down, or there's something upstream of it, a Ferrous metal that's rusting, thus producing Ferric Oxide and dribbling down the pipe and into the cell. Is there any on the upstream side of the cell?
If not, then it has to be localized to inside the cell.
Another though is that you have a very high iron content in your water, mixed with the electrolysis process is causing it to oxidize on the anode, where it combines /w oxygen molecules in the water to form rust, Fe2O3.
This would keep it localized to the cell, and not be upstream, only at the cell, since that's the catalyst, or source and slightly downstream as the flow of generated Ferric Oxide tapers off.
This shouldn't effect the Ti plates though, just simply clean them with MA and you're golden!!
Ti is virtually indestructible, so they should be fine.
EDIT: Hayward says to submerge it just to the top of the cell, so the wiring harness, the electronics on the cell are not touching the acid, coiling the harness may be helpful prior to immersing. 4:1 dilute, 1 gallon of water to 1 quart of MA. And remember, always, always add the acid to the water, never, ever the other way around.
The manuf. says to soak for a few, then rinse with a high pressure hose, then repeat if needed, until the plates are clean.
BTW, Acid attacks Oxides, including Ferric Oxide.
Full thread here
Salt product in water electrolysis