It's reasonably common for a Planetary Governor to be a "King" of their own little fiefdom, in the sense that they are intellectually and culturally elevated above the general populace. There's some mentions of Governors of Feral or even Feudal Worlds who live in a spire or even orbiting space station with Imperium-equivalent technology, rather than live among the savages over which they have dominion.

Which makes sense - it can't be possible to rule an entire planet using Dark Age-level technology for sending messages and the likes, and certainly not for interstellar administration when it comes to things like tithes. Governors get appointed from whoever holds the hereditary title, or otherwise holds favour with the Adeptus Terra so they're not particularly inclined to BE a Feral Worlder themselves.

As such, they probably have contemporary knowledge of Imperial culture, up to and including employing their own Astropaths and Sanctioned Psykers. The easiest why to find out if someone is a Psyker is just to have another, confirmed Psyker look at them - get a lineup of suspected witches once every ten years or so, have your "Court Magician" look 'em over and send away the ones that are just mutants or otherwise unlucky enough to be picked up by the local PDF/Militia/Whatever.

The governors who *are* Feral or Feudal Worlders and have comparable technology probably use a more informal process of bringing all of their suspected witches to the designated Black Ship pick-up area, and the Sisters just grab the ones who freak out and go insane when they walk by.