OB associations are the prime star-forming sites in galaxies. However, the detailed formation process of such stellar systems still remains a mystery. In this context, identifying the presence of substructures may help in tracing the footprints of their formation process. Here, we present a kinematic study of the two massive OB associations Cygnus OB2 and Carina OB1 using the precise astrometry from the Gaia Data Release 2 and radial velocities. From the parallaxes of stars, these OB associations are confirmed to be genuine stellar systems. Both Cygnus OB2 and Carina OB1 are composed of a few dense clusters and a halo which have different kinematic properties: the clusters occupy regions of 5-8 parsecs in diameter and display small dispersions in proper motion, while the haloes spread over tens of parsecs with two to three times larger dispersions in proper motion. This is reminiscent of the so-called line width-size relation of molecular clouds related to turbulence. Considering that the kinematics and structural features were inherited from those of their natal clouds would then imply that the formation of OB associations may result from structure formation driven by supersonic turbulence, rather than from the dynamical evolution of individual embedded clusters.