My turbo/CVT combo actually responds pretty quickly to putting your foot down, and even faster in "sport" mode. My other car has a pretty responsive automatic too.
I once drove a 5th gen Camaro 6.2 and punched it from 25ish MPH, and it had at least a full second delay before commanding a downshift into what I assume was first. Modern tuning really is a "your mileage may vary" game.
