Of course they have started, but they will not kill the new queen. If they kill, you have not select a proper time to introduced the queen.
Normally the new queen destroys the queen cells.
If the mated queen has layed under 2 weeks in the mating nuc, 30% put of queens will be replaced with hive's own emergency queens. 1) But if the queen has layed 4 weeks, it is very rare that it is replaced.
But you should inspect the situation, do they kill the queen cells.
That is my style....
But if it is August in my country, and there is no food in flowers, it is 80% propability, that bees do not accept a new queen. So I change them during winter food feeding.
1) Australian research