Senario:

My Ship has determination and a ship in range 1 has DTF

A crit gets through, does determination and DTF Trigger at the same time allowing me to reveal the crit, then assign it to the ship I want?

I'm guess i'm curious if you get to look at the crit before assigning it to the ship you want.

No, DTF triggers when you have an uncancelled crit result. This is before you actually deal out the cards. So no peeking!

Dice Results turn into damage, which turns into cards.

Draw Their Fire moves a result, so it happens well before you see the card (or even have to suffer the damage).