We study how the stellar velocity dispersion within the Scorpius-Centaurus OB association (Sco-Cen) has evolved over approximately 20 million years, from its formation to the present day, by investigating 32 stellar clusters in Sco-Cen. Using data from the Gaia mission along with supplementary stellar radial velocities, we identified a surprising sequence of abrupt jumps and intervening plateaus in the evolution of velocity dispersion correlating with times of star formation bursts. We find that the association is almost isotropically expanding and that star formation propagated from inside-out with a speed of about 5-6km/s. We measure a present-day expansion rate of about 10-12pc/Myr and observe that younger star clusters within the association exhibit higher velocities compared to older ones. This result, along with the stepwise increase in velocity dispersion over time, suggests a structured and sequential star formation process rather than a random one. This phased evolution suggests that stellar feedback is the primary driver of Sco-Cen's star formation history, expansion, and eventual dispersal. Our findings emphasise the value of precisely characterising stellar populations within OB associations, particularly through the creation of detailed, high-resolution age maps.