I use it in both ways.
1) I use the threat map as it is designed for myself, as MC. I use it as a pragmatical tool to remember threats in directions they are going. It's more an organizational tool to me: I know which particular threats I have to keep in mind when they go there. Much more useful than fronts to me, I don't use fronts, even if i'm using ideas from the "Threat Analysis" threads. I generally don't write what kind of threat it is, as I have index cards for that, just a quick reminder of what is where and how they move (I draw direction arrows).
2) I think I read this advice in Dungeon World or something related: on the Region map we draw together, I add "traces" of some of the threats. Can't remember where I read this but in DW it was something like "if one of your threat is a troop of orcs marauders ravaging the region, draw a burnt village not far from the PC's location". So they don't know it's "The Horde", or the "Fire Cult", they know there's has been the sound of an explosion there, and refugees there.
So PC can see real traces of threats on the map, but only the MC can see the threat map. My goal is to preserve immersion.
[Edit: some details]