It works both ways.
Horror Marks:
The manual is correct about horror marks, which is an attribute that a unit can be tagged with (certain items cause horror marks to the wielder, there's a battlefield spell that you can cast to mark your enemies, and anyone who has ever been hit by a horror will be marked).
Horror Marks never go away. You can re-summon a dead pretender who was marked and he's still marked. Someone can send your Ice Demon to Kokytos and he finds his way out of there and back into your service - he's still marked. You can have affliction removing effects making all your dudes really healthy - doesn't change horror marks.
Horror Marks (like Horrors) come in levels of severity. Higher level marks call nastier horrors, and call them more often (?).
Horrors:
Horrors are monsters that have a chance every turn of attacking anyone who has a horror mark (depends on the mark I think).
Horrors are always independent units (I don't think you can enslave them - has anyone ever taken control of a horror?). They attack anyone and everyone present when summoned, but they are more interested in those with horror marks than they are other units.
Horrors can also be summoned as a battlefield spell by mages - also mages with the correct paths (both astral and blood) can remote send horrors at any province as a ritual.
When a horror shows up in battle (because someone summoned him) he will attack people with marks first. Then he'll just attack closest (though he may seek out mages with astral paths after killing everyone who is marked but before switching to attack closest).
When a horror shows up because of a horror mark, the event works like a commander assassination. The horror faces off against the marked unit in a 1 on 1 fight and usually whoever faces the horror dies. If a really buff unit was horror marked (a kitted out thug or SC), that unit might kill the horror and survive, but usually gets hit once or twice (horrors have armor negating attacks - your protection won't help you) increasing the level of the mark. Horrors will now be summoned to assassinate that unit more frequently and they will be nastier horrors. This keeps happening until the unit dies. The horrors will never stop coming, they'll only come bigger, badder and more frequently.
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Mashup of Terminator series and Horrors from Dom3:
-Cyberdyne Systems Model 101 [Lesser Horror]: Sarah Conner?
-Sarah Conner: Yes
-CSM 101 [LH]: *stab*
(Sarah Conner survives somehow.)
-CSM T-1000 (Horror): Sarah Conner?
-Sarah Conner: Not again!
-CSM T-1000 (H): *stab* *stab*
(Sarah Conner survives somehow - it's good to be the lead.)
-CSM T-X (Dream Horror): Graaaahh!
-Sarah Conner: Oh sh**!!
-CSM T-X (DH): *STAB* *STAB* *STAB* *STAB*
*Sarah Conner dies*
Sarah Conner: Time! I call time out! What the?! I mean, didn't we alter the timeline so these guys aren't going to keep coming or whatever? Is my script up to date?
-Director: Uh, no, you've got the correct re-write. The horrors don't actually care about timelines - they can exist in all timelines simultaneously, past, present and future. They come from this other dimension and - uh, basically, once you're marked you're terminated. You know, they can't be bargained with, or reasoned with. They don't feel pity, or remorse, or fear. And they absolutely will not stop, ever, until you are - you get where I'm going with this, right?