The concept is pretty simple The dye sub ink will only adhere to only the polyester fabric or a ployester coating. There are specialty made 100% polyester shirts or hard substrates that already have a polyester coating on it. If you have a shirt that is 65/35 - 65% of your design will stick to the polyester and 35% of the design will wash away. If you have 100% cotton, then basically no dye sub ink will adhere to your shirt. Hope this helps.
Dye sublimation describes the process of a material (ink) that goes from a solid state, directly to a gas, without becoming a liquid first. Applied heat causes the reaction. Sublimation ink is printed onto a special non absorbing sublimation paper. Epson printers are the most common for this task as they use a piezo-electric process to spray the ink, unlike HP printers which use heat (heat at this point destroys the process). Your image is then pressed onto a special substrate (polyester) which has a porous surface. The heat causes the pores to open, the ink becomes a gas, filling the pores. The material cools, closing the pores making the ink part of the material.
The items you press sublimation pictures to, must either be coated with a special sublimation substrate, (mugs, tiles, wood, etc) or be a material that will accept and retain the ink, (poly, plastic, etc.).
The washed picture looks very faded compared to the original. And if that is only one wash then I can't imagine what it will look like after 10 washes. Look at the red headband adn the red helmet to see what I am talking about.