If you submit the PTO and the same is not shown in the Manager ID for approvals, it is because the PTO Manager is not added for you in the TT User screen in Salesforce.

There is a field as PTO Manager in the TT user screen, add your PTO Manager name to this field and save the changes. Once the admin adds the PTO Manager for you in Salesforce, the PTO's requested by you appear in the PTO request screen for approvals.