It damn well does state how it affects the attempts, in the very next sentence. The attempts are treated as being in a 4-point Background Count.
Not really. Not the "attempts" are treated as being in a R4BC, but the character with astral hazing. It only states that the BC has an effect, if a spell is cast on/at that character, it doesn't state what effect.
A character not in a BC area himself never gets a magic reduction, not even if he targets his spell there. It doesn't say so in the Astral Haze description and it doesn't say so in the BC description.
Besides, why the hell would they feel the need to specify anything about how the Background Count generated by Astral Haze works if its behavior was identical to a normal Mana Ebb or Domain with the same count?
1. The behaviour is identical to Mana Ebb or Domain only for the astral haze character himself or for people very close to him, so they are still in that BC area he creates. People standing a few meters away are not influenced by it. Why should they?
2. SM says that every magical thing (spell,focus,spirit) that enters a BC gets its force reduced by BC rating.
We have those two possible effects considering BC. Astral hazing only says, the attempt to cast magic
on/at/near the specific character is affected, meaning
only when the spell enters the BC. Couldn't that effect not be the one described in SM? Why would you want to reduce the casting magicians magic by the BC rating as if he stands in the BC, when he actually is not.
And, finally, yes your interpretation bloody well does conflict, because right after the word "on" is the word "AT". Don't even try to tell me that isn't meant to cover indirect combat spells, since those are about the only single-target spells where "on" doesn't apply.
Of course indirect combat spells get reduced as well, all spells that enter the BC.
But if there is an indirect area combat spell cast to outside of the BC, while the astral haze character is still in range of the spells effect(only the physical part), then it would not reduce the force of the spell.