Yes, кем is the instrumental of кто.
As for the words choice in the phrase, well, this is what we say when asking what someone's job is.
Кем ты работаешь? - What's your job? or What do you do?
Also, when you answer this question or just states what your job is you need instrumental after the verb работать as well. So this is where the instrumental comes from.
Я работаю поваром - I work as a cook
I hope this helps