I've never done this tour, although I have watched it from dry land.
I am pretty certain that some type of rainjacket is provided. That doesn't guarantee that it will keep you dry, though. I suggest dressing in layers, no cotton (I've heard it takes too long to dry), with a water repellent jacket as your top layer before donning the jackets they give you. And, bring a change of clothing.
By the way, I saw your ship, Explorer of the Seas, in Boston today. She sailed away about an hour ago.