It's an honorable and noble belief. Many would prefer to escape the consequences of their actions when they could. Jon has never been that way, which is perhaps why he carries some of the weight of a future he hasn't lived yet (he's learned to let go more, but there are still moments).

What she says worries him... for her.

"Do you have to bear those same consequences if you haven't acted yet, Josie?" Then he shifts gears slightly, because he's not certain what she means. After all, he doesn't think his own will come for him in Hell (unless Daenerys wanting to murder him counts). "What consequences?"