The javascript is way to advanced for me to understand completly, but I found these bits…
UserStore.COLORS = ["#FF0000", "#0000FF", "#008000", "#B22222", "#FF7F50", "#9ACD32", "#FF4500", "#2E8B57", "#DAA520", "#D2691E", "#5F9EA0", "#1E90FF", "#FF69B4", "#8A2BE2", "#00FF7F"];
util.array = {
pickRandom: function pickRandom(array) {
var randomIndex = Math.floor(Math.random() * array.length);
return array[randomIndex]
}
};
SessionManager.prototype.getColor = function(username) {
var color = this._users.getColor(username);
if (!color) {
color = _utilJs2["default"].array.pickRandom(_usersJs2["default"].COLORS);
this._users.setColor(username, color)
}
return color
};
It would seem that the color is instead chosen at random once, then shown to everyone the same way. If that is the case, I cannot retrieve the color through IRC 
Edit: For anyone interested, this is the js: http://www-origin.justin.tv//tmilibs/tmi-v3.re573acc4d735bfa354884de17021be6d117b2ae5.js (I recommend unobfuscating)