A similar thing could be said for the Angel of Death: people are dying around the clock, and yet the Angel of Death is always on time!

Shaytan is a similar example - he can act on and be aware of many people at once, regardless of where they are located, without infringing on divinity.

Moving along from these morbid examples... My understanding is that once the soul leaves this world, it is not subject to the same restrictions of physical reality that we experience here (such as regarding space and time).

That could especially be said for those who have a high position near Allah, as well as other created beings which do not primarily exist on earth, such as archangels and the ruh.

Possibly they are able to "stretch" into various places at once while remaining in a place near Allah.

This is my understanding - Allah knows best.

In any case, this particular belief does not require ascribing them a divine attribute, although people may accept or reject the belief, or accept or reject the explanation.

It is a good question however!