"How are you doing at home?"
While technically it does not specify, I do think it is often implied to be plural.
Often an interaction would consist of several greetings in succession, and this would be asked after already inquiring about the individual ("hujambo?") So to follow with the singular "hujambo nyumbani?" doesn't make much sense.
Very few people that I met in Tanzania lived alone. When I heard this said (it was pretty common), I think the question meant something more like, "How is everyone (including you) at home?" It doesn't literally mean, "How are you (singular) when you (singular) are at home?"
Not sure if I'm making any sense but I hope something in this rambling mess helps someone!