关于非谓语动词

Being /Doing..., 这种形式强调前后两个动作同时进行
Having been/done，强调前后两个动作先后发生

Looking at the wall, he said nothing.
他看着墙壁的同时，什么也没说

Having finished the homework, I went shopping.
做完作业之后，我出去购物。

在你给出的两个句子中，be tired 是一种状态，“工作一天后很累，Ruth整晚待在家里”“be tired”的这种状态是一直伴随“spend the evening”的，即他晚上在家时一直都有累的感觉，所以应该用being tired

而第二句如果用having been tired的话则意为他已经累完了，就是现在不累了，那么与后文整晚在家，就没什么关系了

tired by a hard day's work与spent the evening home为同时发生的因果。因此要用Being ....。
而Having been 句型表示有时间差的的因果。例：Having been given enough money，Jake could buy the toy plane.

应该没错吧

也许是
having been tired by a hard day's work, ruth had spent the evening home