Lol exploded into tiny bits?
All we saw him do is disappear, people only came to the conclusion he was dead and gone due to the fact that he does not show up in the game at all after that and how he acted before vanishing that time, I'm one of the ones who believed this as well.
But I don't know how he is alive, I'm one of the people who believed he died as well, but his last appearance in DMC1 did not give him a concrete death as shown in the video I posted above, here is a guy who knew how to vanish and disappear as it is, he could have just did that there although in a more dramatic fashion.
And it taking place before DMC4 could open the way for NEW demons for him to fight, we know his mode is not going to be that long as is, for all we know Capcom could simply wip up a couple reskins for the monsters and call them something else and bam, new demons in Fortuna before Dante and Nero even got there.
But from a story perspective if this is canon for him to have that Yamato it has to before DMC4 since I highly doubt Nero would give it to him after the events of DMC4.