Just want to make sure I got this right: when you roll initiative the number rolled doesn't actually come into play. The only thing that matters is whether the die is red or white.
Or does the number rolled on initiative modify Reflex somehow?
There is no roll. You could use red and white stones, or pennies and nickles, or cards that say attack / defend, or anything. They are merely tokens representing a binary decision. The choice to use dice as the token is presumeably because they'd be convenient items that you'd have handy at the game table already anyway.
Yup.