If the fabric and transfer media are matched, they are run through a set of heated pressure rollers at around 400°F (about 205°C). As the material passed through the rollers, the heat causes two things to happen simultaneously. First, the pores of the polyester fabric expand and open. Second, the dye from the transfer paper is converted to a gaseous state and the pressure from the rollers forces it into the open cells of the poly fabric, thus infusing the color to become part of the fabric itself.
For sublimation printing ,we all know cotton and polyester fabrics are generally pretty durable, and for use in a parade, I can't think of any reason or usage, rain, snow, sun, or whatever, that would hurt a polyester poplin fabric banner. The dye sub print process permanently infuses the poly fabric with color during the print process so that you can send these banners through the washer without color loss, and a rain storm would be more gentle than your average washing machine, we'd think.
This process is somewhat like photo printing in that the tones are continuous, unlike the dot pattern of an inkjet printer. This also is what creates the richness of color, tone, and continuity in dye sublimation printed fabric graphics that catch everyone's eyes.