i have the exact problem, i beat her viewed the cutscene and when i went to exit the instance the game D/c. i came bk and was unable to complete the quest cause i think alphinaud is still outside the howling eye and theres no way to get bk there without cids airship. i killed her again to see if i land outside but it just teleported me bk where i was before i joined the duty finder.
hope this gets fixed am setting at 50 just dying to finsh the story quest off and start with my relic quest