The mite you can see in your hen house..alhough red..is bird mite = northern fowl mite. There is some sources that call it red mite..but it is not proper name.
There is pest for the plants that is called Red Spider Mite, but those have nothing to do with birds.
If you can see red mites in your hen house..those are mites that have already fed from you birds and are full of their blood! Those mites that haven't fed yet you will struggle to see..so don't assume you've got rid of them..I would reapeat the treatment again within 10 days from the last treatment.