Strange feelings

For the most part, her past and your past need not be talked about. Does she keep bringing up her "first" or do you bring it up? If you do, just stop bringing it up. If she keeps bringing it up, then I think the two of you need to sit down and really discuss your relationship because to me it would indicate that she is not yet over the other guy.

I can't say it better then that other than the feelings the OP is having is called jealousy.

or make her your first to talk about with smb else.

This is terrible advice. He has every right to ask her not to talk about her ex to him.

After that, if she keeps talking about her ex, then it would be a show of disrespect on her part (if it's not already - it may currently just be thoughtlessness. There's not enough context)

Ignoring her talking about her ex would just invite the same thing to occur again down the track. If it bothers him this much, why would he want to leave the possibility open that she would bring up her ex again?