KHR timeline

I was thinking tonight, and for some reason the sound theory about how the timeline of katekyo hitman reborn worked started to crumble. So I have a few questions. I used to think that when tsuna and the gang beat byakuran the TYL Tsuna would no longer be dead. But I mean how does that work? In the future that the gang will live in be different because they defeated byakuran? What are your theories?