His obsession basically boils down to three things: 

1. The Master Watch – is an heirloom passed down through the men in the honorable Hakuba family line. Technically, Hakuba’s father – The Superintendent General Hakuba – should have taken possession of it when his father died… but when the grandparents disowned Saguru, claiming that the marriage between their son and ‘that foreign tart’ was not sanctioned in the first place (they eloped), and refuse to recognize a half-blooded bastard children as a rightful heir, Hakuba Sr stole it and gave it to Saguru, anyway.
   He is proud of his son and thinks that he should be happy to be a part of the Hakuba family, even if it means that their branch has been cut from the larger tree. Oh well.
   Hakuba is pleased to show it off at every heist, case,  and interview, proving that he is doing great things and IS a part of the family, whether they like it or not.

   You can read more about the Master Watch here: The Seven Sins of White Chapel: Envy

    

2. Eidetic Memory is a Bitch –  Hakuba’s memory is like a steel trap; very accurate, very detailed, very easy to recall… but along with it comes every other sensory input – sight, taste, smell, feeling, emotions… Most of the time, he’s able to extrapolate just the vital information in terms of data that he can use in paperwork, but it requires a lot of self-discipline and work. Sometimes, however, the ‘flashback’ of memory is so intense that he loses track of what is happening in the present. It all works in tandem with PTSD , and those experiences can be quite triggering. 
   The watch helps with this in two ways:
   First, it acts as a physical anchor that he can use, with ritual to ground himself in the present. This helps to stave off anxiety attacks and more traumatizing memories that he doesn’t want to be forced to live through. 
   Second, it allows him to accurately record the data for the CURRENT situation, which he then compares to his wrist-watch, then records in his notebook. This way, he doesn’t have to rely on only his memory for analysis, which he is quite picky about. With careful note taking and accurate records, he feels much more confident in his work and control of the situation.

   Learn more about Eidetic Memory here: The Seven Sins of White Chapel: Lust

   

3. Accuracy as a Scientist – Since Saguru has been shown to be at least a passable chemist, interested in the work and equipment in his grandfather’s private laboratory in Japan, it would stand to reason that he would be used to keeping very accurate notations for every experiment. After all; a single digit can change the entire outcome, and the scientists in the labs do all that they can to check everything to extreme measures of precise calculation.
   I think this is why he sometimes includes the milliseconds, etc. when he’s notating the time to others; it’s a habit of working with scientists… and quite possibly humorous to him, since it really is excessive, but some take it quite seriously.