After upgrade, laptop requires two logins, two separate accounts to get in

I recently re-provisioned a Macbook Air laptop for my use. It's a custom-built machine that is only a year old. Previously, it had two user accounts on it: and Admin account and second user account that also had admin rights.

In the re-provisioning, I:

• Deleted the second user account
• Created a new user account for me with admin rights
• I logged into my new user account, and in the setup, selected restore/set up from Time Machine backup

This completed, everything looked great. So, while logged into my user account, I deleted the old Admin account. Everything is fine. The machine is renamed under my name, etc.

The first time I rebooted my machine following an install, the log in popped up, and it was as the old Admin account. I thought "Oh, did I not delete it?" Then after a few seconds, my user login popped up. I logged in, FireVault ran its scan and I am back in my familiar desktop. I checked the Users & Groups in Syst Pref and there is no "Admin" user but I have to login as Admin on a reboot before I get to my login, nonetheless. I can live with this, but if someone understands what happened here, and how I could resolve, would be much appreciated.