尻をたたく is an idiom, sort of like English "kick in the pants". Consider:
My lazy little brother never does any work until someone gives him a good kick in the pants.
You wouldn't interpret this as literal brutality, just forceful reminding/urging. Same goes for 尻をたたく, at least in this case, and you can tell because of context: it just seems really unlikely that modern-day training materials for a nice upper-middle-class test like JLPT(N1) would present stories of someone's brother getting literally beaten by unnamed third parties simply for being lazy.
I also think that when talking about someone else's butt in the context of literal butt-spanking (i.e. not using a set idiom like 尻をたたく) you would tend to use お尻, not just 尻.