Lagging vs. Leading Indicators and Market Reaction

I'm trying to solidify my understanding of how leading vs. lagging indicators really influence immediate market moves. While I grasp the theoretical difference, it feels like sometimes the market reacts strongly to a lagging indicator's release (like a surprising CPI print), even though its data is already old. What am I missing about how traders reconcile that 'old news' with current positioning, especially when the Fed is so data-dependent?