New user

I host a number of domains. With a number of users. No problem thus far. There is a user who whishes to make
databases and subdomains himself. Lets call him userX. No problem. I grant him my plan: Billing --> Account Privileges:
Billing: none
Grant Privileges: none
Dedicated Servers: none
Domains: only his own
Users: none
Groups: none
Mailing Lists: none
Databases: none
Plans: My plan

UserX logs in to the webpanel. Makes a new user. Let’s call him/her userY. UserX grants userY shell access. Now userY can access all the directories of all my users.(UserY can’t edit anything but can copy files to his own computer.)

Does anyone know how I can prevent userY from accessing these directories? Many thanks in advance for any reply.
Couldn’t find this problem anywhere in the discussion forum.