when you think about it right..Jack must have seen his compass pointing to Port Royal at the beginning so thats why he didn't go there....and then he learns Liz is in danger from Will and he mentions the compass to him. It suddenly clicks in Jack's head that he cares for her and guesses that his compass is pointing at her when he looks at it...But right now he's like "I want to SAVE MYSELF!"...
If he had no clue where his compass was pointing to after this realization, he would have gone to the location it said wouldn't he?..but he knows its pointing slap bang at her so he doesnt follow it (or does he? "off to Tortuga" and guess who is heading straight there as he says that)...when he's sitting in the Tavern he's trying to make it point to where he thinks it should point instead of where his heart is telling him..he says "I KNOW what i want!" and he waves his hand infront of it to try ane make it work...maybe he thinks that if he can get Liz with him his compass will start to work for him? Because if he gives his heart what he wants then the compass should point to where he wants it to..