Several fibers are used in felt hat making.  The most common fiber would be wool from sheep, a natural fiber.  The wool is not spun nor woven, instead high temperatures, some agitation is applied and then the fibers are dipped in cold water which forms the fabric that cannot be easily pulled apart.  After the felt is made into a hat, it is ready to be dyed.

Mixes and blends of finishing grease and coloring powders is used by the manufacture of the felt hats for dying.  A specially mixed powder, matched to the hat color, is hand rubbed into the body to enhance a more even tone.
Specified amounts of ingredients, such as oil and lanolin; refines the dye powders.  They use blended powders, according to color they desire.

Usually hats are dyed 3 or more times to achieve the proper color.  Some fibers accept dyes more readily than others, so at times, the color may vary.

If a hat appears to have color variances on the hat after cleaning, it is because of the powder dying process.  In those lighter areas, the powered dyes have lifted some.  This is applied at the manufacturer level, and cannot be duplicated by any cleaner.

Outdoor astrosphere can also change the colors; such as UV rays or sun fading causing the dyes to oxidize.

Attached are informative materials on the process of over dying natural fibers.