It does double the residue, but modulo 19. 2 * 18 = 36 = 17 (mod 19) and 2 * 10 = 20 = 1 (mod 19). The reason is that the method consists essentially of two steps. (1) Subtract a suitable multiple of 19 to make the number a multiple of 10. (2) Divide by 10. And dividing by 10 is the same as multiplying by 2, since 2 * 10 = 20 = 1 (mod 19).

Well, it does double the residue:

20 * 2 === 40 === 2 (mod 19)

21 * 2 === 42 === 4 (mod 19)

18 * 2 === 36 === 17 (mod 19), equivalently -1 * 2 === -2 === 17 (mod 19)

10 * 2 === 20 === 1 (mod 19), equivalently -9 * 2 === -18 === 1 (mod 19)