Why time in the cage for the Queen matters:
Did you know that in spring/summer adult bees live an average of 4-6 weeks which is about 28-42 days. You don’t know the ages of the bees that were packaged, but let’s say they average 4-5 days old. Some will be older, some younger, but on average they will be fairly young. Let’s add three days for shipping and make them 7-8 days old when you receive them. Now let’s say you add 7 days holding time for the queen, which means the workers are 14-15 days old before the queen is released.
The released queen may wait a few days before she starts to lay. Let’s say 3 days. Now your workers are 17-18 days old when the first egg is laid. So now add 21 days before the first worker brood starts to emerge. Now your original workers are 38-39 days old. Recall that your spring/summer workers are going to live an average of 28-42 days.
Release the Queen while workers are young:
What is happening is that your original package has almost died off before your new bees start to emerge. Your colony will take a huge dip in population during this period in any case, but the longer you wait to release the queen, the worse it will get.
You want to have enough bees to care for the queen, build comb, prepare the nest, feed the larvae, defend the hive, keep the brood warm, collect water, pollen, nectar, and propolis . . . and perform all the other myriad hive tasks. So, although you want to be reasonably sure the queen will be accepted, you don’t want to run the colony numbers too low. This is why most suggest that you estimate how long the bees have been with their new queen, and then add a few days until it totals about 5-7. In my case, I estimate 3 days in transit and add another 2-3, then I release the queen.