이미 and 벌써 are normally used as the same meaning. The sentence, "그 사람은 이미 학교를 졸업했어요", can be used when both speaker and listener know the fact and only speaker does. When both of them know that, the sentence has the meaning of 'as you know'. And when just speaker know the fact, the sentence gives listener new information about someone graduating already. And actually 그사람은 이미 학교를 졸업했어요 and 그사람은 벌써 학교를 졸업했어요 can be used at the same situation.

The important thing is that 벌써 includes a sense of surprise while 이미 is more flat and factual. 이미 only applies to something that is already past (이미 늦었어요). 벌써 on the other hand can be used for things happening now to mean it's sooner than you thought. So 아니, 벌써 세 시야! (Gee, it's already 3 o'clock!) is natural, but 이미 세 시야! sounds weird. Because of this, 벌써 tends to be used more widely than 이미, especially in daily conversation. Explaining it by only one person or both persons knowing it doesn't seem the right way to me.

Thank you so much!