作为领导(没做过领导的没什么发言权),对属下是否要问?

我朋友她的领导问她
"how are you doing otherwise?" She said "fine." he siad, "well, that's not really convincing."

he kept asking and looking at her. then she told him, "well, my hu*****and and I have seperated."

这个领导做的appropriate么?
我们做领导, 发现属下有情绪异样, 是否要关心的询问一下?