Only you and the person you are talking to in a one-on-one chat can see your conversation. Private conversations are just that, private, even if you have them in a corporate application.
Account administrators or teams and/or groups in Ommnio cannot see the private conversations you may have with other users.
In the hypothetical case of a labor conflict, you should know that conversations in Ommnio are the property of the organization and that, by legal requirement, the company may request access to them.