Tafashshi means spreading. It belongs specifically to ش (shin). During its articulation, air and sound spread through the oral space in the characteristic manner of this consonant.
Practice: pronounce «أَشْ» correctly, then contrast it with «أَسْ». Both involve hams, but ش has tafashshi whereas س has safir as a notable distinctive feature.
Converting shin into sin or artificially sustaining shin is not the aim. Tafashshi describes the letter's inherent sound, not an extra consonant or vowel added to the recited word.