It's kwangu because nyumbani (with the -ni suffix) is a place, and places are described with ku-, mu- or pu- (correct?). So ku-angu = kwangu, referring to the place that is my home. I think that's one of the most important lessons of this exercise, and it took me a while to grasp.
But if you're welcoming someone to your house, you must be in your house-- so the house is near and specific. Ku- refers to a "general/non-specific/far away place" according to the tips. So why isn't it "pangu" or "mangu"? I don't get how one chooses the correct prefix with possessives.
The TUKI dictionary says the opposite:
nyumba = house
nyumbani = home
So the correct translation ought to be "Welcome to my home".