That would be a good trick unless you're using Direct Sail, and even then you'd soon notice the difference. Turks is pirate, Tortuga is French, so you'd be facing the fort at both of those and probably wouldn't live long in the little ship with which you start the game. Starting from Barbados, you'll hit Nevis before you reach Jamaica, though you will be able to land because the pirate settlement has no fort.Look at your map. Port Royal is on Jamaica. It sounds like you missed Jamaica and ended up at Nevis, Turks, or Tortuga.
But yes, what was Redmond island is now Jamaica, and what was Redmond town is now Port Royal. If you've found a pirate town then you're not on Jamaica.
I've also found that pausing the game does not work. If I want to stop for any reason to do with real life, I either press F1 (Load/Save/Options menu) or F2 (Character/Quests/Inventory etc. menu), either of which will stop the action.