I can clarify one thing for you: the UCI number starts with a T because it is a temporary number assigned to all up front medical exams. I had one too, I was asked to do further tests even before sending in my application (I did the medical exam in Oct. and I was able to send the complete application in Nov. due to some problems with translating my PCC). So don' t worry about not having AOR yet, the medical assessment is done separately by the CIC doctors, not visa officers.
Another thing I can tell you is the fact that your email came from NDVO is not that weird. The office that deals with the medical exams is a regional office. For example, all medical exams in Europe are being assessed at the London VO. This is where my request for further medical tests came from, and neither I or my husband have any ties to the UK.
I recommend you compy with this request, or you risk your application being denied. The fact that the doctor was able to access your eMedical file and tell you what exam CIC requested is a good thing and there is nothing weird about it. My doctor was also the only one who could see that too.