Getting in between another teacher and his student One subject I teach is also taught by another teacher at my university. Usually we do not both teach this subject during the same semester but sometimes we do. Students do not get to choose their teacher, the are assigned into one class or the other.

This has introduced a strange dynamic in that some of the other teacher's students have come to me asking for information about the subject, since they know I also teach it. So far, I've been quite hesitant to answer any such questions because I am worried about getting in between the other teacher and his students. I can imagine that I might have an answer that is different than the other teacher (perhaps my answer is wrong, perhaps my answer is right, and perhaps both of us are right but we have different ways of looking at a problem). The issue is compounded by the fact that I am from the West but the other teacher is Asian so there are cultural issues at play here (and I'm in Asia so it's not my culture).

I imagine this would be less of an issue in subjects like math where there is a specific formula but in management subjects the perspective of the teacher can change things significantly, especially if one teacher might be less strong in the subject than the other.

So, what should a teacher in this situation do? Refer the student to their teacher? If they feel they cannot get an acceptable answer then refer them to a search engine? Should I jump in if they feel they are lost and their teacher is not helping them understand (this seems like it could cause serious problems, even if handled well)?
My first question is, why are you (the faculty) both teaching the same class at the same university without talking to each other?  I can understand the cultural differences, but this is even more of a reason to talk to your colleague about the class!

I would suggest (as posdef does in his comment) to talk to the other instructor about the class, offer to have him sit in on your class, and ask about collaboration.  You could also ask to sit in on his class if you'd like, but you need to be careful to phrase your request so it is clear that you're there to gain insight into his class and not to provide criticism.  I can't tell from your comment, "...if one teacher might be less strong in the subject than the other" if you believe he is the weak one or if you are, but regardless, you can both learn from each other.

Finally, it is in the best interest of both classes of students that you collaborate with the other instructor -- if both courses are listed as the same in the course catalog, the students should be able to expect that the class will cover roughly the same material.