So this is the POD: somehow the Europeans developed naval technology two or three centuries ahead than OTL. Thus between 1150 until 1250 they already have ships that able to cross between the oceans.
While the premise is that they want to go to the East in order to finding helps against the Muslims. With the funds from the King of England, King of France, and Holy Roman Emperor, as well as the blessing from the Pope, the European joint expedition fleet set sail in late 12th or early 13th century, and arrived in OTL Caribbeans.
Now, would this better or worse for the Natives? Keep in mind that the Europeans haven't mastered gunpowder yet.