Say I play a Noggle Bandit (or any card with split mana in its cost). Does its color depend on what mana I use to play it, or is it always both red and blue? It seems a little weird that this card would return Aurora Eidolon from my graveyard to my hand AND be able to block red creatures with intimidate if I only paid blue mana for it, but I highly doubt that it would 'remember' the mana-color used to play it. Likewise, Reaper King would always be 5 colors no matter how I pay its cost, right?
A card's color is all colors contained in its mana cost, be it regular mana symbols and/or hybrid and/or Phyrexian mana, plus the color of its color indicator, if any:
Also, it's not at all unusual that a card has a color that is different to what you pay to cast it. There are numerous cases where those two properties are unrelated.