Depending of the quests... In gathering quests for example, you always receive of a certain color. For example, the botanists receive their first kurta red. Miners dark blue, fishers cyan-light blue.

I think every quest that gives you items have already set a color, (It seems especially made for make the character look awkward until you have abbility for dying, nya!) Some quests show you the color before giving you the item, others show the item like if it would be without dye, but then when you receive it, it's already dyed.