I think that's a bit strange, because the 50 minutes should be set aside for you, and you will lose some of them by coming late.
If I were you, and I had already agreed to this, then I would do it once and then make it clear that you don't want to do it again because the full 50 minutes should be for you to spend with your T.
Btw, when I started therapy I used to start getting extremely agitated and nervous 2 days before my session. By the day of my session I couldn't focus on anything. I used to arrive 2 - 3 hours early, and then I had a series of little walks I would do and coffee shops I would visit in the area of my T's office, until it was time for my session. I realise that is a bit extreme! But it didn't harm anyone!