The most common ways user’s access Chrome extensions are by using their Chrome User Profile or the Default Chrome Profile on the device.
(If you are Logging into your Google email it is not the same as logging into Chrome and you would need to have extensions setup through the Default Chrome Profile on the device)
Chrome User Profile:
When a user logs into a *Chromebook or Chrome Browser they are loading their Chrome Profile onto the device. As long as their settings are set to sync, any Extensions installed under a User’s Chrome Profile will follow them from device to device when they log into Chrome.
Default Chrome Profile:
When you do not log directly into the Chrome Browser on a device you would be using the Default Chrome Profile. You would have to install the extensions on each of these devices through the Default Chrome Profile.
*Chromebooks that are set up with a default login would be using the Default Chrome Profile on that device.