That client is not set up to be "Pool Exclusive." This means that if it has nothing to work on in its own pools, it will start to work on jobs that are in pools to which it doesn't belong. This is a preference in how you decide to use the pools.

To change this behavior, open the Client Settings dialog for the client in question and check the Only render jobs in my pools check box. You can see if a client is pool exclusive in the client list of the main window.

Pools are actually saved by each client as a list of the pools to which that client belongs. If you delete a pool, but a client that belongs to that pool is off-line, next time that client starts, it will still think it belongs to that pool, and will re-create the pool with only itself as a member.

To avoid this, make sure that every client that belongs to a pool is on-line and connected before you delete the pool.