Counterions in adsorption of ions
Since this got no answers, I'm posting an answer from Reddit user midnight-cheeseater, which can be found here.


  There are two main possibilities here, depending on how the ions are adsorbed:
  
  
  If the solid only adsorbs a type of ion, either positive or negative. Such as the example quoted of alumina adsorbing fluoride ions. The alumina will become negatively charged at the specific points where the fluoride ions stick to it. These negative charges will attract anything nearby which is positively charged. So the $\ce{Na+}$ ions will associate themselves with the negatively charged areas on the alumina.
  As a solid adsorbs one ion, it may release another. This process is commonly seen in ion-exchange resins. Such as those which are used to produce "de-ionized" water. These adsorb positively charged metal ions and release $\ce{H+}$ ions at the same time. They can be regenerated by running fairly concentrated nitric acid through them.
  
  
  The counter-ions are typically chloride, sulfate or nitrate, as well as some other halides, carbonate and phosphate. So this essentially converts a dilute solution of metal salts into a dilute solution of hydrochloric, sulfuric and nitric acids. Which explains why "de-ionized" water is rather acidic, as opposed to distilled water which is neutral.
  
  Another common example found in dishwashers and water softening systems is an ion-exchange resin which adsorbs $\ce{Ca^2+}$ or $\ce{Mg^2+}$ ions while releasing $\ce{Na^+}$ ions at the same time. This converts dissolved calcium or magnesium salts (usually bicarbonates or sulfates) into sodium salts. These are regenerated by running saturated $\ce{NaCl}$ solution through them, which is why dishwashers and water softeners require a supply of salt.