The fact the supernatural powers sporting humans are organised rather loosely like this, in the guilds operating for nothing but personal glory and money, more or less, leads to weaknesses. While the groups in the guilds can work, at least theoretically, in small units to face stronger dungeons and bosses, it's still no military force where every detail is created and trained to function as a part of a much bigger army. The S ranks, especially, don't really need to work that much with others, and when they do, I reckon it's more a bunch of strong individuals working for a common goal, but also competing with each other, than a cohesive force. Even in this operation, which isn't the first against the ant island, the whole strategy is extremely simple, probably because anything more complicated would have zero chances of working, with such headstrong individuals. Even this isn't so efficient because the hunters, due to being strong individualistic fighters of different types, aren't genuinely combining their power. They were merely given places where to fight, but they act like it's every man for himself.

Normally I'd say Jinwoo is behaving irrationally because if the ants win and infest the mainland, it's not like his mom and sister could keep living peacefully. But at the end of the day, he could have probably cleaned the island on his own, so he doesn't need to take it awfully seriously. At least as long as he believes the S-rank hunters can pull it off, even if they need to struggle. Furthermore, like MFauli said, he can appear on the island immediately if things seem to go south.

It's another question whether he should feel so relaxed simply because he saved his mom.