I thought about that too, but to be honest, I'd like to also think the object that sends you back in time finds its way to Ban after his lover "suicided" if that's the case. Who knows what becomes of lonesome Ban if it is travelling through demensions- though maybe those numerous "futures" get erased after going back in time every time. Or maybe they were created like little branches from a big branch but oh well. It'd be a shame if the fortune teller didnt at least explain he was just jumping demensions & even if he did jump dimensions, he'd be going "back in time" in those demensions, so really, it feels unnecessary to assume it's dimensional. Who knows.
No I think its just a time travel not a parallel Universe because if its parallel Universe their life situation should be different to original one like ban is only his bestfriend or ban is already married to someone else or he might become one of his relatives or just a stranger to him.. For me that's a parallel universe so please dont think such a terrifying possibilities it will make me cri ಥ_ಥ

Well, this is just my opinion and it is not stated by the mangaka, but I've been thinking that instead of Ii-chan being time travelled to the last, I couldn't stop thinking if he was actually travelled into a parallel universe or something like that and then after leaving the previous universe(jumping off the 2nd highest building in Japan(⊙…⊙ )), Ban would live a life without Ii-chan in that universe.It'd make me feel more sad towards both of them (/TДT)/. Btw, this is the result of watching time travel anime(aka jumping into parallel universe). Last but not least, this is only my thought and it is not applied in the manga because the term"parallel universe" is not stated. WELP, the story just make my heart shattered into pieces (/TДT)/. It's gonna take time to recover from it ╥﹏╥ (/TДT)/ ╧╧