That's how it is in our hospitals as well. I won't identify my program, but neither the fellow nor the attending are in house overnight for any of our primary services, including our ICU. I'm (as a PGY3) cross-covering 20 ICU patients right now, did two lines so far tonight, and have seen three consults that I made the decision whether they'll be coming to the unit overnight. I denied one of them a transfer to the unit, and my decision stands as definitive until the patient is staffed in the AM. The only other person in-house for ICU right now is the PGY2 I'm on with, and she's covering the other half of the patients. Not doing consults currently as we're trying to alternate days to allow the other to leave early, but tomorrow that will be her job. We spitball ideas off each other. Both fellow and attending are available by phone if necessary and both are rarely called. That said, they will come in if asked.
For our floor patients, theoretically the on-call attending can also be called at any time. I've never heard of anyone calling them. There is also a different academic attending technically in-house covering their own patients (a service our attendings round on when they're not on our academic teams) that is available if the PGY2+1 covering the floors have any urgent questions or need supervision for a procedure, but that attending is rarely utilized. I can count on one hand when I called them when I was covering wards at night last year, and that's because it was one of our chiefs that I was asking to supervise me doing a procedure as a favor. If the floor cross-coverage people really need urgent help, they walk across the bridge and consult with the residents covering the ICU service. Otherwise, we learn how to take care of our patients and present them the following morning.
Edit: Oh, and we're responsible for all the code blues in the hospital too. Including the ones on the completely non-academic hospitalist services. The hospitalists, who aren't our faculty, stick around long enough to give us a blurb on why the patient was there... and disappear mid-code.