It's all explained to you on the DL website. The issue is not whether she is a minor, it is her age. As she is travelling on a separate PNR, DL has no way of knowing whether she is a UM or travelling with a responsible adult, e.g. you. DL will want you present and will confirm that you have boarded in order to assure that she is not a UM who has not paid the $150 fee and is also not evading other restrictions on routes which UM's can't fly.

https://www.delta.com/us/en/children...ravel/overview