List Manager in v16

Hi

This might be a really simple thing (sorry) but does anyone know how to enable users at a lower permission user group level to generate lists created by a System Administrator? All my new lists made since we went into v16 are only viewable by other users unless they sign in as system administrator? When I log in using a lower level user group, I can still generate and access them presumably because I am the creator. They can copy the list and then generate it but surely there should be a way to give them access to generate my original list. Is there a security object I am missing somewhere? Although I dont necessarily want them to be able to edit the list, only generate it. Any help would be greatly appreciated.