Thanks Alexander for some insights!
From what you have described, I understand that something is wrong with the fact I am NOT
getting Kerberos ticket on login.
I'm guessing I should investigate SSSD logs to see what might be happening there.
I am meant to be using most default setup, didn't modify anything and my intention was
not to get it manually. I'm still trying to get my head around those things as a
mortal user, playing with ipa at home :)