You're inexperienced with poly, so I'll give you a break
But that's very limited thinking. There's no reason why the secondary has to be submissive.
I started out as a secondary; there was a D/s dynamic, but it had nothing to do with the status of the relationship. It was simply new. He now considers me his co-primary (he has another primary). I am still submissive to him.
I'll say this, though, his other primary had the exact same thoughts as you: She felt I should be submissive to her since I had secondary status.
2) Just because I may be submissive to your partner does NOT mean I have ANY relationship with you, let alone a submissive role. She was pretty annoyed when I didn't obey her the same way I obeyed him, though