In theory, no treatment is necessary after fixation of the color particles when using disperse inks. However, not all fabrics intended for direct printing are the same. There are many different pre treatment chemicals available to textile manufacturers and they all have different effects.
Two of the most common treatments that cause users headaches are silicone-based and soap-based treatments.
With a silicone-based treatment, the sublimation dyes are attracted to the oily silicone coating as well as the polyester fabric. Over time, excess dye residue on the fabric will leach into the coating and migrate away from the image, forming a colored halo in white areas around things like lettering.
Soap based treatments, in contrast, do not migrate like silicone. Instead, the excess dyes become lodged into the soap. When a soap treated flag comes into contact with water, the soap acts as a dispersant and begins to run, carrying the excess dyes with it. This can give a printed flag the appearance of the inks "running", even though the fixated portion of the ink remains static.
In both cases, the easiest way to eliminate the above problems is to wash the fabrics immediately after fixation, before putting them outdoors. A gentle detergent is necessary to remove the remains of a silicone treatment, while a soap treatment will wash out immediately with water.