I'm guessing that the reference to "racing against time" in the 2nd Scenario Special Rule is meant to invoke the Time Pressure Victory Banner Objective rule on page 8 of the Expansion rules.
Time Pressure Victory Banner Objective - When Time Pressure
rules are in effect against the attacking player, he is racing against
time. The defending player, after playing a “Scout” Command
card, may draw 1 Command card and take 1 Permanent Victory
Banner instead of drawing 2 Command cards at the end of his
turn. Taking a Permanent Victory Banner is not possible, if doing
so would give the player his final Victory Banner to win the battle.