I surprised myself by being on the other side of this recently.
I would always have said, tell the ex first - and no introductions anyway, until it's "serious".
Well... First up I introduced them really quickly. He has a son the same age who lives with him, so we thought it would be nice to do stuff with the kids - and also it was practical. It would have been really hard to find time to see each other, and we didn't want to leave our kids with babysitters. We made a judgement call about our kids personalities and understanding. My 4yo met my bf about 4x before I told her he was my bf. I broached it saying "I really like him - I think I might ask him on a date". She said "cool - mummy, he might be your one true love!" (blame Disney!) It's a particular set of circumstances and children, and I think we made the right decision. I'm confident that she would cope fine if it ended, I haven't got him acting like a daddy all the time (he's just the same as other friends we hang out with), I'm as serious as you can be about someone early on, and I don't intend to introduce her to a new man every 3 months for the next 10 years! If this doesn't work out, the next man, even with exactly the same situation, would be kept away - just to manage turnover!
As I said though, if asked at point of split, I'd have said it was too soon!
And if my ex introduced someone this quickly... you know what? I'd be unhappy, and I'd judge him. Because I trust my judgement, I don't trust his.
But something I have learned since the split... Behaving well to him doesn't make him behave well to me. If the only reason not to tell her was so he'd stick to the same rule - then no point in bothering, as I wouldn't trust him to stick to it.
So that's telling her.
Telling him first... yeah, I'd have always said I should. He's a lying, cheating stealing arsehole though, so I just found I didn't feel inclined. I nearly did - but changed my mind. It felt like by telling him, it was validating that he had a right to know, even a right to an opinion. Which he doesn't. Like I say - I trust my judgement.
I was in two minds, cos what I really wanted to avoid was her saying something and then being questioned and feeling she'd said something wrong. But, he's pretty uncurious so I decided to just leave it.
I'd just had enough of having any contact with the cheating wanker. In theory, despite his cheating, I wanted to be amicable. I was amicable. Then he decided to steal money from me and I just decided enough was enough - minimal contact. So - chit chat about my life - NO.
As long as my daughter is not affected by me not telling him - then it's none of his business, and I don't want the contact.
Not an opinion I'd have expected to express.
But I thought I'd give my story, for exactly that reason!