That's what a time limit is for. You can of course argue that it is about the starting time of games rather than their end, but that would seem wrong.
If you want to play a rapid tournament for one hour, you shouldn't need to play 1 hour and 20 minutes on top because the game is still going. The only way to get a result after the time is to disregard the ongoing games. Or everyone would have to wait for the last game to see final standings.
The current solution seems mich better than what
chess.com is doing: simply aborting any unfinished games. Here, you can finish your games, and they count for your rating. It's just that they are not eligible for tournament points any longer. Seems the best solution to me.
Not sure of of the exact algorithm here, but you won't be paired very close to the end when it is highly unlikely that you cannot finish in time.