It looks like this particular video was done on a white screen. Look at the woman’s hair at 0:46 as she passes in front of the people behind her.
It can definitely be done either way. Hand drawn mattes or rotoscoping will probably be necessary if you use a white screen. Lots of green fringing and spill will be visible against white if the green screen isn’t perfectly lit and keyed.
On a budget, I personally would attempt this against a white screen first. Definitely test and research lighting before doing the real thing.