All boats and ships, when turning, will experience some sort of a heeling moment toward the outside of the turn. The force trying to heel the ship over is the centrifugal force (Fc), and as according to "Applied Naval Architecture" by Robert Zubaly, is a function of the ship's mass, forward velocity, and the turn radius. The centrifugal force acts in a tangential direction to the curvature of the turn at any particular moment. The angle the ship would heel during a turn is a function of the centrifugal force, the ship's displacement, draft, and center of gravity. I'll spare you the math but I can post it if you're interested.
I don't know the exact numbers in the Titanic's situation but my understanding is the Olympic Class ships had a fairly large turn radius when at normal cruising speed, which would result in a low centrifugal force, and that would result in a low, very likely not noticeable, turning heel angle.
I'm sure there are others on this forum who are more knowledgeable than I am regarding particulars with the Titanic, such as center of gravity or exact turn radius.