Each mission is unique, but there are common rules for almost all of them:
Cash Out: Usually, bets where Cash Out is used will no longer count toward the mission.
Voided Bets: If a bet is voided or cancelled, it will not count toward the objective.
Time Limit: Missions have a deadline. You must complete all objectives before the timer expires.
Rewards: Once the mission is completed, the reward (Free Bet, Golden Chips, etc.) is automatically credited.