You seem to be confusing two different things here. He was elected
pope before being ordained a priest. That does not mean he was made a bishop before being made a priest.
If you look at the
Old Catholic Encyclopedia, it answers your questions in the very second sentence of the article on Celestine III:
He was forty-seven years a cardinal when, in his eighty-fifth year, he was elected (30 March, 1191) successor of Clement III; being only a deacon he was ordained priest (13 April) and consecrated bishop the next day, respectively Holy Saturday and Easter.
He was ordained a priest before being consecrated a bishop.