This problem is usually solved by having a separate group of visual development artists develop an overall look and palette for each film before the animation begins.
ðɪs pɹˈɑːbləm ɪz jˈuːʒuːəli sˈɑːlvd baɪ hˌævɪŋ ɐ sˈɛpɹət ɡɹˈuːp ʌv vˈɪʒuːəl dɪvˈɛləpmənt ˈɑːɹɾɪsts dɪvˈɛləp ɐn ˌoʊvɚɹˈɔːl lˈʊk ænd pˈælət fɔːɹ ˈiːtʃ fˈɪlm bᵻfˌoːɹ ðɪ ˌænɪmˈeɪʃən bɪɡˈɪnz.