Did the appointed times of death of all the people who die in a natural disaster arrive at the same time?

Appointed time of death means the end of the time an existent will spend in its peculiar environment and the end of this existents life. Everything that found existence afterwards actually comes to the world with such a fate of end.

In the course of the flow of the existence, it is not possible to differentiate between the beginning and the end. Everything eventually falls down to the earth and melts just like a drop, and like a stream they eventually flow and meet a sea.

This is the common fate of almost all existents. With this fate, every being comes into existence and again with this fate it leaves away as it came.

In this world, both births and deaths take place each as an exhibition and as a test. Just as everything coming into existence is a clear proof of a secret Existent, their leaving this world at the end of the appointed time also indicates the eternity and immortality of this secret Existent who has no beginning. Certainly, we and everything that have come into existence from non-existence and nothingness show with our existence the existence of the One; with our seeing, hearing and knowing, we show the One who sees, hears and knows; and by leaving aside everything that we have borne for lifes long and going away, we show the unknown ONE in comparison to ones who come one after another and go one after another and who go and do not come back. He Who has created death and life, so that He may try you (and demonstrate to yourselves) which of you is better in deeds. (Al-Mulk Surah, 67:2)

To grasp the mystery of coming, to pass the test of existence and to be prepared to depart; these are what is really important for the human.

Now that we have made this small preparation, let us handle the topic Did the appointed times of all the people who die in a natural disaster come all together?
Yes, the appointed times of death of all have arrived at the same time. And there is no serious and important obstruction for it to happen this way. As the Exalted Being, who has control over the entire existence, creates everything and everyone from the atom to systems in their own fates at the same time, He can also cause them to die at the same time. Neither their being in different places, nor their difference in quality and characteristics may cause any obstruction.

All in all; the existents with different nature and characteristics continue their lives facing the Sun without causing any disorder; they take on all colors under its light; they flourish with it and with its rise and set, they become paler and finally fade down. Just like that, everything is germinated in the lap of the same spring; everything flourishes in the same summer and they turn pale in the same fall; but all their fates are each different. All of them exist and continue this existence not recklessly or spontaneously but in the direction this Exalted One wishes and wills, with the plan and program of this great wisdom and with the guidance of His endless will and wish. He knows whatever is on land and in the sea; and not a leaf falls but He knows it; and neither is there a grain in the dark layers of earth, nor anything green or dry, but is (recorded) in a Manifest Book. (Al-Anam Surah, 6:59)

While the lives and deaths, growth and fruits of trees, grass, seeds and grains are watched that much seriously, can such a perfect existent as human ever be left alone to wander as he pleases? The Exalted Possessor of the worlds, whose seeing something else is not hindered by seeing something; and whose hearing something else is not hindered by hearing something, surely gives importance to every state of the human and bestows upon an individual what He has bestowed upon the kinds and species of other existents and thus He treats the human, who is the index of the worlds, exclusively and will grant him His special reward and will honor him in His presence with His special call.

As a conclusion, death and the time of it are only the termination of the time of staying in this world and paying service. Such a time is like a plan that is prepared beforehand, registered, and written down in such a way as not to annul the will of the human; and it is nothing but the carrying out of it when the time comes with the command and decree of the One who sees and knows everything. There is no reasonable difference between its being collectively and individually.