Actually, the ten breaths' time Yusuf Zuck spoke of was not for Roger Benson and the others; he said so to delay for ten breaths. After all, Leonidas King's life or death was unknown, and Dail, who shot quickly, was still in the city. Therefore, Kase Day got in touch with Dail, and with Dail's speed, if he couldn't find or rescue Leonidas King within ten breaths, he would confirm Leonidas King's death. Hence, he wanted Guard City to disappear forever.
He didn't know whether his secret had been spread, but he was certain that Leonidas King, who had been captured, had definitely had his Space Ring inspected and his soul searched. At the very least, Eden King's father knew his secret, and that Arellano Family Goddess might also know his secret!
Therefore, he came with the intent to kill, because he knew that once his secret was leaked, he would be doomed with no redemption, becoming prey for countless people.