There were lots of reasons why the Immortal Leopard was so furious at Corey, and one of it was because the injuries he caused to him would require him to use his Immortal Mana to heal himself, and he had been preserving his Immortal Mana because the quantity of Immortal Mana in the world was extremely limited.
This was another reason why he did not use his Immortal Mana to chase Corey and Pamela. He only used his physical strength and speed which was not at its optimal state because of the injuries he suffered at the destruction of his world.
He believed that with his physical strength and speed, he would be able to catch up to Corey and Pamela who were just Tier 3 and Tier 4.
But with every second that passed, he realized that his current speed was shockingly not fast enough to catch up to both of them.