When exactly does timing start? The rules say "Timer starts as soon as the screen focuses on the intro screen". So is 0.00 when the black screen fades into the pixelated screen where mario stands or is 0:00 a little bit after when the black text box starts appearing?

Start timer at -3.20. Doing that will start right when you start to control Luigi.

To follow up on what MCRikki said, if you use the -3.20 timer start, you should then start your splits when you press "Player 1 Game". 3.2 seconds will go by before you have control over Luigi.

This is the easiest way to start your splits at the correct time.