During the play of my first two games I have missed my turn because the first player finishes her/his turn a second before the round time limit of 24h. There is no way to get a first turn this way.
you are talking about freestyle seq games?, ok when you end your turn, you have to wait till your opponent starts OR wait 12 hours, so looks you weren't online in those 12 hours you had time to play
OP, all of your games have been Sequential so far. In Casual Sequential, you have 24 hours to make your move. (I know it says the round length is 24 hrs, but that means each player has 24 hrs.) Just make sure you check your games a couple times a day, and you won't miss your turns.