Hi.
Sorry for your loss.
Why do you believe mites is that killed your "rooster" and how old was he? I highly doubt that's what it was. Hard to know for sure without a necropsy if the mites contributed to the death. Depluming mites are often deadly by the time those are caught but they are invisible to the naked eye. Seems to me like there was more going on than meets the eye.

And when I spot mites on my birds NEVER worry about it causing death to occur. They are a common parasite found on many birds.
Permethrin spray is very safe, affordable, effective and easy to use. Though in freezing weather would consider using dust even though I absolutely don't like dusting as it poofs every time they shake out.
If you experience another death, necropsy is highly recommended. Link to achieve that...
https://www.backyardchickens.com/threads/how-to-send-a-bird-for-a-necropsy-pictures.799747/
https://www.aphis.usda.gov/animal_health/nahln/downloads/all_nahln_lab_list.pdf
I would ask more questions to really get at the root of what happened.. How old is the rooster, how many birds total in how much space, what is fed including treats and supplements, any new birds recently added... how was stool and appetite? What symptoms presented before death?