I wouldn't even assume that mathematics undergrads understand manifolds. I think the majority our math majors never see the definition of one before graduating, and only a small handful could actually tell you the definition (manifold is actually a really tricky notion!). In fact, one can even finish our "graduate prepatory track" without encountering the notion. We do have a differential geometry elective which probably contains the definition, but is focused on submanifolds of Euclidean space. In the US, I think outside of a few top places, it's not regarded as a standard part of the undergraduate curriculum; manifolds and their basic properties are the first thing covered in our graduate topology class, and I don't think we assume that students have any experience with them.
Very serious theoretical physics students may actually be more exposed to manifolds, since they take general relativity, but I doubt that actually includes much interesting exposure to the notion (since generally, they'll work in Euclidean space).
I think it's unlikely that any other large population of undergraduates is getting exposed to them; I certainly have never heard anything that suggests so, though of course, it's hard to rule it out happening somewhere.