Animated Texture doesn't begin at first frame

going off of your first link, the problem lies with this line:

     var index : int = Time.time * fps;

Time.time goes off of the time the game started, what you want is to start with zero.. to do this ,we can zero out the individual time on creation.. just change/add the lines:

     var framesPerSecond = 1.0;
     var myStart : float;  //add this line

   function Start(){
     myStart = Time.time;   //add this
   }

 
   function Update(){

            var index : int = (Time.time-myStart) * framesPerSecond; //change this
   }
   

this way, we account for the amount of time that has passed between the game start and the creation of the object :)