Extensions automatically update to the latest version, except for partial rollouts to a subset of my user which are labelled partial rollout in the Changelog. Those changes may take 1-2 weeks for everyone to get the update, or you can re-install the extension to force it. (Not recommended) The Changelog contains all the information on updates.
Go to chrome://extensions > checkbox Developer Mode > Update extensions now
Partial rollout updates
To force this update you must re-install the extension or wait about a week for Jason to push it out to everyone.
If you are using my Gmail extension you get notifications on updates of your choice in the options