An epiphany is an event where in a flash a person realizes the truth of a situation or when something that made no sense or that was thought to have no significance is suddenly understood all at once.
The Epiphany described in the New Testament was the visitation of the wise men to honor Jesus when he was a small baby. That was a moment when the outside word first began to understand Jesus significance and Jesus and Mary were confirmed in their own beliefs.
Another epiphany that Mary and Joseph experienced that caused them to believe that Jesus was quite unique and was called to do something special occurred when they visited the Temple as a small boy, and he participated in the disputations that learned men were having there, and stayed in Jerusalem at the temple even when his party was returning home.
Novelist James Joyce especially generalized from specific events reported in the Bible to other life-significant events that were interesting to a storyteller or novelist. See this article on epiphanies in Joyce and Wordsworth's work.
If you hear someone using this phrase in conversation they likely have literary or critical training. Qualifying it as a "first-person epiphany" is evidence of this particular writer's cleverness. This whole phrase is not common usage.
If you used it, you would have to likely have to explain that you mean a flash realization that a person has about his own situation or predicament.
Might be OK to use epiphany in the vicinity of a University or among friends who were writers, English students or divinity school atendees. Could get you heckled or worse at a sports bar.