Mmh, nah.. he wants to level up ASAP because how can he help people if his strength isn't enough? There was actually some explanation on his side in the novel. And ofc he wouldn't pass up the chance to face the bastards who nearly killed him.
Besides, it was Japan's affair. He's still under the jurisdiction of the hunter's association, not to mention he's the one who discovered the plot those Japanese made in Jeju.
However, as he stated in the novel, the Japanese hunter's assoc deserved to be abandoned because of their wrongdoings, but the innocent people doesn't deserve to die. That's why he went there..
actually his system dungeon key has a limit too i believe, he has to enter it within the time frame when the key activates and imo finding about where his power originates is important as well considering what cha hae in said about his power (and the japanese kinda reap what they sow with them setting up the whole jeju island raid so....) *shrugs*
I get peeved when Jin-woo hesitates to help people because with his strength and shadow warriors they can prevent so many unnecessary deaths, I know he's eventually going to be there but a dungeon break is more imminent (not important) than Finding out about his powers
If there is a dungeon break in Tokyo, millions of people will die but he can learn about his powers later