Using the Cup of Reincarnation means that there would be no casualties from the Cataclysm and most of all, the chance to see his father again. He has lost too many people. But Jinwoo considered that leaving the earth to fend of otherworldly threats or pursuing the Chaos army in the gap between dimensions would leave the planet vulnerable. This variant of Jinwoo had thought further ahead on how to deal with the potential threat of other Itarims, though he is aware that there was much that he has to prepare for. Perhaps it is better to get some help. Maybe it is better to have the hunters protect the people, rather than letting them forget everything about the cataclysm. There is another alternative he would like to take.....though it may be difficult, it is possible.
The Jinwoo from the original universe likely also considered the risk of leaving Earth behind to defend it, but thinking that he was the only one who could handle it, he took it on alone. The Jinwoo from this timeline, though, decided not to use the god's tool and instead fix things from here.