Permissions settings

I need help about permissions because I can't really understand the mechanics by myself.

I want to create different vaults with different access, like:

• VAULT-A
• VAULT-B

In Azure AD, we created different groups for our users, like:

• vault_a_contributors;
• vault_a_managers;
• vault_b_contributors;
• vault_b_managers.

We have set no vaults permissions under "System Permissions" settings, as we understand that those will applied to all vaults (a sort of default root permissions): is it right?

Under each vaults, we set group mapping to roles (f.e. in VAULT-A, vault_a_contributors > contributors).

We tried some users but member of (f.e.) vault_a_contributors can't see the vault.

Moreover, should be possible to manage different permissions between folders inside the same vault? For example:
VAULT-A
|__________FOLDER-A (some users)
|__________FOLDER-B (some others)

If yes, how?

Any help?

Thanks.