I have the same type of storage under the sun visors. Originally it came with some self tapping screws - that won't hold. Did a proper 6mm bolt going thru the headliner, backed by a large piece of sheet metal to spread the load and keep the headliner in good shape.
The front mounting tabs of the storage goes in under the mounting points for the sun visor.
Tested it on a couple of months worth of horrible corrugated roads in Morocco and Iceland. No squeaks - rattles or any deformation.