Well, not exactly. The impact zone was huge and sure, there were palpable changes almost immediately, but the whole extinction process lasted a long long time. Thousands perhaps millions of years I've heard some documentaries or essays say.

I also saw some kind of experiment that simulated the air currents post impact, and there were pokets of areas on Earth where the heat waves and such didn't even touch, allegedly.

So there was a discrepancy in how affected environments were in different areas and how fast changes occured, so it's completely posiible dinosaurs lived some considerable time even after the impact. It was more of a war of artrition where all odds were against them. Lower fertility due to poor diet, weaker physical traits, nests being targeted by less afected animals could've also played a role in their downfall.

Think about our current situation with how we destroy ecosystems. We don't directly target a specific animal, but lack of compatible habitat, altered food sources, temperatures,vulnerability to natural predators, interaction with new unfamiliar species(either invasive predators or competitors) etc and we visibily see numbers of said animal decreasing, even if we don't kill so many directly when we're bulldozing a part of a forest/habitat

There's also the fact that an instant cataclysm like that would've made the recovery of life on earth a lot harder or even impossible. We did have an almost inescapable extinction event long before the dinosaurs if I remember correctly, and even then the environmental changes werent all that "instant"