Well, no one replied and I was no longer able to reproduce the breakpoint being hit 3 times, although I'm sure it happened a few times.
And yes, appcache or html manifest caching works in a different way than regular caching.
With the first visit a page, that had the manifest attribute on its html tag, the same page being listed on the manifest made a request to the server for the same page.
I'm making the answer a wiki in case someone wants to add anything.