I dream about PrevT often. For me, it usually means I miss her and it's time to get in touch with her again. I haven't dreamt of current T yet, that I can remember.
You might want to go by how you feel...you are doing well..excited about starting a new job and chapter in your life. Maybe a little of the anxiety and excitement about the new job is coming out in your dream?
I know I tend to over-think things. It's hard, but try not to read more into your dream than that.
When do you start the new job?