Fatigue works the same way in the TOC as it does in a SimLeague with one exception: the TOC begins as if it were the 26th game of the season where each player begins having used up a prorated percentage of their available plate appearances or pitches thrown.
For instance, a hitter had 500 plate appearances during the actual season. An additional 10% is added for padding, bringing him to 550 PA.
When the TOC is started, the first game is treated as game 26 and he begins having used up 25/162 of his plate appearances, or 85 plate appearances.
Pitchers work the same way for pitch count.