I'm sure parts of the government would keep track on Buffy's location at various times. Riley doesn't ask her why she's working there because 1) He is mission focused and 2) It's kind of none of his friggin' business.
I'm sure he remembers how things ended between them and doesn't want to seem nosy regarding her non-slayer life or impose himself. He's there for slayer-Buffy, not to chat with his ex.
Riley specifically tells Buffy that he's there tracking a scary demon. He's on a tracking mission.
He should've clarified that they shouldn't kill the demon until it leads them to its nest/eggs or whatever; that mistake is on him but he's juggling the awkwardness of working with Buffy and such.
I think he probably didn't see Buffy sleeping with Spike coming, despite what the conspirators might claim. So I'm sure Riley knows very little about Buffy's current circumstances, the fact she died for a while, things like that. Nor does he know about Willow being 'off the magicks' or Xander's engagement.
There's plenty of stuff he doesn't know about current Sunnydale, clearly.