Who started the other fight club chapter?

It seems pretty clear that it was Tyler. It's possible that some of these chapters were self-starting but Tyler often kept the Narrator in the dark, even lying to him whenever he wants... but the the script has the Narrator (called "Jack" in the script) say..

Every city I went to...

...as soon as I set foot off the plane..

...I knew fight club was close.

Tyler was setting up franchises, all over the country.

Wikipedia seems to confirm..

Seeking Tyler, he begins to discover that Tyler has established a secretive underground network of fight clubs nationwide operating under the ethos of Project Mayhem.

The denial you refer to..

                        JACK
            Local 8 just started in Penns Grove.
            And, Bob said he was at fight club in
            Newcastle last week.

                        TYLER
            Newcastle?  Did you start that one?

                        JACK
            I thought you did.

...is, perhaps, the first indication, in hindsight, that Tyler is the Narrator.

I'd like to remind you one thing/scene here(couldn't find the web link for scene but will edit with timing of the scene).

Remember Narrator gets angry when he came to know about Project Mayhem and argues with Tyler that he din't inform and din't make Narrator a part of the project. In reply Tyler says he tried to help him but he's not hitting the bottom as Tyler wanted, so Tyler alone taking care of Project Mayhem without Narrator intervention. And Project Mayhem requires franchises all over the country. Tyler started franchising when Narrator is asleep(without letting him know).

So I agree with your second point but in different way i.e Tyler Durden started the chapter without letting his host know so that he could achieve something's his host could never and he doesn't want in anyway that his Host destroys the actual plan at same time teaching Host what really it's all about.