I am not sure I understand your question, "what does a DUI look like on the record?" If you are on DUI diversion then you do not have a conviction and will not if you sucessfully comolete the diversion. Diversions do not appear on your driving record, only convictions. However the test failures appear there. You insurance company will be able to find those. You can go to the Kansas Department of Revenue web site and purchase a copy of your driving record.
Legal disclaimer: Patrick M. Lewis, (913) 558-3961, firstname.lastname@example.org. www.TheKansasDefender.com This answer is intended to provide general information about the justice system. It does not provide legal advice nor does it create an attorney-client relationship. It does not provide the basis for making decisions about a course of action. Legal advice requires more communication and information than is possible in this format. Many important considerations and factors need to be investigated and discussed before an attorney could give legal advice about this issue. Before making any decisions about a course of action readers are strongly encouraged to contact a lawyer and secure an attorney-client relationship. Readers must also understand that this format does not provide for confidential communication.
Typically a DUI incident will involve two different types of entries going onto your driving record: the end result of the criminal case and the up front revocation of your driver's license for failing the test. It sounds like you were able to avoid the first mark from hitting your driving record by getting the diversion, but that doesn't keep the license revocation from staying on your driving record. That's what you're seeing where it says ".15 or greater" on your driving record. The diversion can't make that go away. You would have had to file a separate legal challenge to the license revocation to have the chance of getting it removed from your record.