The criteria for getting the eyes of fire is that you had to have accepted the 3rd job instructor's quest to fight zakum before you start the free eye of fire thing. Pretty much every class can get them except the Sengoku characters (or they can if they can get the zakum quest from someone else, I dunno, I didn't check that much) I have all of the classes you mentioned, and have gotten the free eyes of fire as long as I went and talked to the job instructors about fighting zakum beforehand.
"The souls I reap never see heaven. They never find peace. Nothing awaits you but despair! - Gig (Soul Nomad)