When the manga starts Shinkurou is already taking care of Murasaki and you really don't have any idea what the hell is going on and why this loli is around. Other than he's supposed to be protecting her; but you know nothing else. (No father, nothing with her mother dying, etc)
Most of the chapters are like one-shot stories of Shinkurou going out to save/protect someone and then one chapter goes into his past but that's about it. If anything the manga timeline is taking place somewhere in the middle of the anime. Though the things going on with Murasaki in the manga vs the anime makes that a little more difficult.