If the player is not an operator, no players appear in the tab when entering /open .

Without OP:

With OP:

At the same time, players without OP, have openinv.*.

Cannot reproduce. Please try on a clean installation of only OI. Also would need things like server and OI version. Also, bear in mind that OI's permissions are capitalized, and some permission plugins are case sensitive. You may have misconfigured your permissions as a result.

For testing without any plugins other than OI, you can add this entry to your permissions.yml:

basic:
  default: true
  children:
  - OpenInv.*