I often like to scrutinize rules by looking at extremes.
Pregame coaches/captains conference: "Hey BillyMac, I'm going to want a thirty second timeout at the first dead ball after the two minute mark of the first period". BillyMac, "Sure coach, let me write that down."
Also extreme: Team A has the ball in their frontcourt. Team A coach, "Hey BillyMac, I want a sixty second timeout after we score". Team A doesn't' score. Team B gets a rebound and moves upcourt where they shoot and miss. Team A gets a rebound, moves upcourt where they score. BillyMac: "Sixty second timeout granted to Team A". Team A coach, "No, I wanted it back then". BillyMac: "You said you wanted a sixty second timeout after you scored, and you just scored".
Or: Team A has the ball in their frontcourt. Team A coach, "Hey BillyMac, I want a sixty second timeout after we score". Team A doesn't score. Team B gets a rebound and moves upcourt where they shoot and miss. Team A gets a rebound, moves upcourt where they score. No time out is orally or visually requested, nor is one granted. Team B inbounds the ball, easily breaks the hastily set up full court press, and moves upcourt. Team A coach, "Hey BillyMac, I said I wanted a sixty second timeout after we scored, and we just scored. What's the story?".
I'm not a big fan of taking time out reservations in advance, just walk-in timeouts.
But If a coach preorders (sorry, mixed metaphors), I will pay close attention to get his timeout granted in a timely manner.
Again, when in Rome.