I don't know what determines when the treaty starts, but it varies. I have had it as Portugal in the 1520s, earlier for other nations.
Side note - I tried playing the Inca for fun. Got a random event that Cuzco had become Catholic (good missionaries, I guess). So I edited the save file, changed my religion to Catholic, started actually researching tech, and changed my pagan provinces to Catholic by the random colonists I received. The Pope must have been pleased.
Then the Treaty kicked in. All my provinces had Spanish shields on them, and they were just waltzing in and taking them without a DOW. I imagine the Incan emperor was quite pissed off that he had converted....