Gravitational wave is caused by the abrupt change of movement of massive object through spacetime. I would imagine the two neutron stars are traveling to each other in way slower speed than the speed of light. When the edges of the two neutron stars first touched, their movement was abruptly stopped and the gravitational wave propagated out. The light only went out after the merging of the two objects, the compression, and the ignition of the kilonova, which took some time.