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Your sensor is reporting data using the North-East-Down (NED) convention commonly used by aircraft. ROS messages assume the East-North-Up (ENU) coordinates more often used with ground robots. This should really be documented in REP 103, but is not explicitly mentioned. For a (long) discussion of ROS navigation satellite conventions, see the sensor_msgs GPS API review.
Multiplying by a constant quaternion should rotate your data from one frame to the other, but I don't have a good enough intuitive feel for quaternions to give you the exact multiplier. A little experimentation should suffice. Basically, you need to rotate Pi radians about the x-axis followed by -Pi/2 radians about the z-axis.
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