The Day Before Tomorrow is a wonderful take on Time Travel. The reader shouldn't focus so much on how Ichigo got back in time, as apposed to what happens after. Such, usually, is the case with all Time Travel fanfics. The real beauty of this story is how Ichigo, being Ichigo, manages to get himself into quite the weird situation with Aizen by being an Attack Now, Think Later kind of guy. The subsequent diverging from cannon spirals into a really very clever, well-thought-out and honestly badass chain of events that leads to all sorts of fun and interesting scenarios and character development.
Including, but not limited to an interesting take on Ichigo's Super Powered Evil Side, Kon serving an actual purpose and Tatsuki being manhandled by a Hollow.
If anyone reads any of the authors previous works—particularly those that focus on Ichigo's inner hollow, then they'd understand the sort of odd personality (as opposed to cannon) that he takes on. It's not bad, not at all, just a bit different. Everyone else for the most part is COMPLETELY in character.
And it's all Urahara's fault.