It looks like there was an issue with that button still appearing even if they don't have the permission. I've posted an update to the repo to fix that.
To set edit, publish and delete permissions for a module, you must specify them in the module's config like so: 'permission' => array('edit' => 'my_module', 'publish' => 'my_module_publish', 'delete' => 'my_module_delete'), Then you must create those permissions in the admin and assign them to the user.
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To set edit, publish and delete permissions for a module, you must specify them in the module's config like so:
'permission' => array('edit' => 'my_module', 'publish' => 'my_module_publish', 'delete' => 'my_module_delete'),
Then you must create those permissions in the admin and assign them to the user.