No stupid questions here!
You don't roll separately for Fallout. Instead, anytime a Bird rolls for an action and takes stress, they compare the highest rolled die with the amount of stress they have the the track.
So let's say a player is only rolling 1d6 for an action, and gets a 4. They mark stress, and then check the highest die in the roll (4 in this case since it's the only die), and would compare it to their current stress score to see if they trigger Fallout.
So to reiterate, no separate rolls for Fallout, just check it with the roll that triggered marking stress!