I have to think an incoming black hole would be hard to detect. A big one will give off minimal radiation because it is a black hole. A small one might give off Hawking radiation you could detect if you were looking in the right way. We could detect a rogue black hole by new gravitation lensing of stars on the far side of it; as that distant light passed near the incoming hole it would bend in an uncharacteristic way and the stars in that region of the sky would seem to have shifted position relative to one another. If your people live in a nebula, the more distant stars might be already obscured / refracted by the nebula so it would be harder for them to notice the difference.
Nebulae have stars inside them and those close stars will be easier for your people to see. If the black hole interposes itself between the planet and a star that star will seem to disappear. They might start to catch on that something was happening.
An incoming black hole will certainly suck in the gas of the nebula. If this is an emission nebula the concentration of glowing gas whirling down the drain of the black hole will make that area of the sky brighter and give away the presence of the hole. If the nebula is just dust this will be more difficult to notice. Even dust might glow as it heats up during its descent into the hole.
Once the black hole gets close enough to the system to start messing with orbits your people will definitely detect it. Things are going to get bad fast for them.