Role restrictions are a Zendesk feature that is designed to allow only a subset of your agents (such as only admins) use a particular app.
Many times during the initial installation of a new app, administrators will enable the app only for a select group.
Tymeshift works best when it's enabled for all agents, because this allows you to monitor and view reports for everyone.
If Tymeshift isn't working for some of your agents, it's possible that role restrictions were enabled when the app was installed.
Here's how to disable role restrictions:
Go to Admin > Manage > Tymeshift > Change Settings
Uncheck the "Enabled" box next to Role Restrictions as shown in the screenshot below.