I think this question might be slightly off-topic... but in case you are really concerned, I think the answer is no.
What you might be seeing is an effect of the Tang powder getting wet before it dissolves fully to form your Tang drink. See this post from the physics Stack Exchange or this post from 'Ask the Van' at the University of Illinois
Things appear to be darker when they are wet, for reasons explained in the posts I linked to (briefly, dry objects reflect more light than wet ones, as the water allows more light to pass through a wet object). So your yellow powder might be appearing as a darker shade of orange, the 'red spots' you see.
Also, if Tang were really putting blood in its drinks, various food standards regulatory bodies would probably notice and stop them from doing it, and there would have to be court cases etc. So keep drinking the Kool aid (or whichever brand you prefer)!