Depending the mass of the propelling body and the distance of the "payload" from it, the ship/probe may experience tidal stress (see Larry Niven's story "Neutron Star"). Otherwise, if I understand the article correctly, the payload would be in "free fall", only
away from the propelling mass rather than toward it.
Depending on propulsion method (e.g. surfing on nuclear detonations), the payload may of course experience considerable "stress" merely catching the relativistic mass in the first place.
It just occurred to me that the article had no suggestions for slowing down at the end of the journey...