Because the same day Mihawk escaped the marines, cross guild was created?
CG was still weeks away from being created
Mihawk himself was fighting marines for days after his sentence "it's exciting to get chased" but next time we see him he's already packing and saying he has to leave because it's bothering him now.
Because Mihawks bounty didn’t get updated after the warlords were abolished
The fact that he became wanted and his bounty was unfrozen means it got updated.