Maybe it was during the Clinton years.
I just know that I never saw colors assigned to parties until then. And I remember Republicans in the news, at that time, questioning why Democrats didn't pick red. It's more suited to them.
I know about the blue dog Democrats but that color did not define the party color because blue dogs were ostracized by the mainstream socialist Democrats because they actually believed in America. The were the Kennedy and Truman Democrats, not the Wilson, FDR, LBJ, Carter, Clinton, Obama and Biden Democrats. The last one was Joe Lieberman.