You are correct that the downdrafts and updrafts are there. But they are currently limited, because people were complaining about being tossed around like a paper plane inside severe convection.
Also, the downdrafts are just that - downdrafts. Turbulence is more like sudden jolts rather than a steady increase/decrease in vertical speed:
https://youtu.be/IKEcA3hNKsQ?t=1244 (20:44 timestamp)