For all MLB games (not including spring training), the listed pitchers must start for your bet to stand. If one of the listed pitchers doesn't start, the bet is void. If a pitcher is changed and then reinstated, it's treated as a normal pitching change.
If an MLB market is offered without specified listed pitchers, all bets stand regardless of who starts. For leagues and competitions outside of the MLB regular season and playoffs, all bets stand regardless of any change in pitcher.
For more information, see the General Rules, Tickets & Wagers article.