Sellers can publish product if permission is given to that seller category.
To do so go to Settings->Permissions in sellacious backend, select seller category in "User Category" and Sellacious in "Component".
Now scroll down and go to Products permission, find 'Activate/Deactivate any Product' and make it allowed.
For more info on permissions visit https://www.sellacious.com/documentation-v2#/learn/settings/permissions
Hope this helps.