As far as I can remember, you get a quest from one of the NPC's in your faction base in the Vale, which leads you to the isle. However I am not certain do you have to do the quests to get to Krasarang area beforehand. But I doubt it.
No rep needed. At least I had practically no rep with the prince when I got to 90 and went to isle with my alt.
I too have had the same issue...
I can't remember exactly, but after dinging 90 on an alt the auto quest didn't pop up for me until a day or two later (maybe even a relog or something)
Best thing is to go to the Shado Pan garrison in Townlong and talk to the npc yourself and see