Red mite do stay on the birds - not all of them but enough to allow them to reinfest if you don't also dust the hens. If you think about it, it's logical, otherwise where would the initial infestation and reinfestations come from? There are bound to be some mites which haven't finished feeding when the hen jumps off her perch in the morning, so they cling on til bedtime. Similarly some wild birds will be carrying a few.
We use a weed wand to burn them out of their nooks and crannies, and every now and then paint the houses inside and out with creosote replacement.