@simonverbois What other roles are the users in question being mapped to?
The access to global tenant is included in kibana_user role, if you remove this role_mapping and provide the necessary access via the custom roles, this should fix the issue you are having.
A custom role who assign to an user read permission on is tenant (this tenant allow a read access to a specific index)
And a bakend role, kibanauser
My final objectif is the creation of an user who have full access on his private tenant (I would like it to be able to create its own index based on that of the custom tenant) and read access on a custom tenant (he can also create some items, like dashboard, saved search, etc.)