Whether he chooses to reveal or is discovered, this happens on the hunter's turn. The way I read that paragraph, he gets to immediately move (4 spaces) and that is all. Then, he picks a character and equipment. I don't feel that the rules suggest that he gets an entire free turn when he reveals. Just a free move.
As soon as the hunters' turn ends, he gets a full turn, and is free to use equipment, powers, and move as normal.
This is the way we interpreted and played it as well, and it seemed to work.