If the matter consists of a loose collection of falling objects, say raindrops, or a group of rocks, then each individual piece of matter will not expand or contract owing to curvature of spacetime as it falls (except a tiny bit as I will explain in a moment), but the distances between the objects will or expand or contract, depending on what spacetime is locally doing. Notice that this prediction is the same as the one made by the more familiar Newtonian picture of gravity: particles falling to Earth are each attracted to the centre of the Earth so two particles at the same height but separated by some horizontal distance will get gradually closer together as they fall. Two particles starting out from different heights get further apart because the lower one accelerates a bit more than the upper one.
The curvature of spacetime is also inviting each individual raindrop or rock to be squeezed or stretched in the same way, but the internal electromagnetic forces between the atoms are resisting this, so the individual raindrops or rocks remain of almost constant size.
When a gravitational wave passes by, the story is similar: separate freely falling rocks will be moved closer or further apart, but the size and shape of each individual rock is hardly affected because the gravitational effect is small compared to the internal electromagnetic forces. However, in an extreme case such as near a neutron star or a black hole then the gravitational effects will overwhelm everything else so that even rocks are crushed in one direction and pulled apart in the other.