If I recall correctly from my interviews a few years ago, 6 months of non-psychiatry rotations during intern year was the standard. I think there may have been a program that did 4 months of internal medicine, 1 month of ED, and 2 months of neurology for a total of 7 months. I also seem to remember one residency program that might have done neurology in the second year. So there may be a little bit of variation.
As for what is expected of you during the non-psych rotations, the party line is always going to be "when on this service you are a medicine (or neuro or emergency resident) resident and will be expected to do everything that you would do if you were training to be an internist (or neurologist or emergency physician)". This is what every program will tell you. The reality probably isn't too far off. In my experience, they expected a little bit less of me in terms of medical knowledge. I would be asked to carry all of the same responsibilities, but they didn't seem as annoyed when I didn't know the answers when being pimped. I do think they leaned on me a little bit in terms of helping to verbally de-escalate difficult patients (which shouldn't be a skill exclusive to psychiatry, but we do become better at it than most over time), but I was happy to do this in order to feel useful.
I'm sure there are some psych interns who have experiences of, say, being asked to see most of the psych patients who come into the ED rather than the chest pain/abdominal pain cases, but I don't think I've heard of any egregious examples. In fact, I had several ED attendings who asked me to avoid the psych cases because they knew I would have plenty of opportunities for that later.
As an aside, as a chief resident I am navigating various resident complaints/concerns via text, phone, and e-mail pretty much daily. Interestingly enough, they're almost never about the non-psych rotations. With that in mind, I would echo OldPsychDoc: choose your program based on psychiatry.