I don't think him showing he had the idol did any damage at all. Before they were going to vote him out which would force him to use the idol and they didn't believe he had. Now that they KNOW he has it, they know that it could be THIER bottom that recieves the second most highest votes and would be less inclined to make him waste it.
Before it was a shot in the dark and they didn't think they could be going home, now they know it could be them going home. It was better for Yul not to let them continue with thier ignorant bliss about the idol. He now has a better chance of never having to use it because they will all be too scared to take the risk