There are 3 reasons a colony would make a queen, swarm, supersedure, and emergency. I ma not an expert but here are my simple summaries.

For a swarm, they plan ahead and normally make drones when conditions are getting favorable to swarm. When conditions are right, queen cells are made and when the first ones get capped, the old queen swarms away with some bees.

For a supersedure, the colony considers that the queen is faulty somehow and they make a few queen cells. I don't see or think they increase drone production. The old queen either gets killed off or can swarm away with a few bees at any time. The new queen can even emerge before the old queen is gone.

For an emergency, the old queen got killed or missing somehow and they build emergency cells from existing new brood in normal worker comb. They only have one chance at the time when there is eggs or very new brood to make queen cells. This is an unplanned emergency so no drones are made ahead.

Once a swarm or emergency queen is made, there's typically a setback of the hive and no laying queen exists, which would end drone production. Drones already laid would continue to emergence normally. Supersedures can sometimes go almost unnoticed in the colony if the queen is allowed to stay till the new one is emerged and maybe mated. Or, the faulty queen hasn't been laying so they are compromised and would end drone production.

 

But I don't see people stating clearly about when a hive decides to make queen cells if that means the hive is also triggered to making new drones at the same time or right after making a new queen?

It's nothing to do with 'being cool' ...
Why on earth would a hive want to produce (more) drones to coincide with a new queen ? Are you advocating that a virgin queen should selectively mate with it's brothers ?

This wouldn't work anyway - as queens take around 16 days to emerge into this world, whereas a drone takes somewhere around 38 days before it's ready to fly out to a DCA.

Drones are not necessary for the survival of an individual colony (which is what emergency and supersedure queen-raising is all about) - only for survival of the species.
LJ

 

Queenless hives tend to tolerate a lot of drones when other hives have been throwing them out.

 

Did I miss the part about spontaneous generation of drone eggs? When a hive is queenless, they attempt to make a new queen from appropriately aged worker larvae. Unless there were already drone eggs and larvae in the hive, they lack the ability to raise more. At least until the hive goes laying worker.