Thank you for the compliment! As to the discrepency though (and for the sake of pre-explanation in regards to the soon coming chapter two):

Although underage magic is recorded at the Dursley residence, the magic of adults is inconsistently registered - I say inconsistently, because while Dobby was registered, several adult wizards were not. The Ministry tracks the use of magic through the Trace Charm, which cannot be placed on an adult. And although the charm is described as affecting the 'vicinity' of where an underage witch or wizard may reside, it is heavily supported in the books that adult witches and wizards can perform magic around an underage child without it alerting the Ministry. The Ministry generally ignores when the Trace is broken by underage wizards and witches of wizarding families, expecting their parents to discipline them, and living in a magical household essentially makes it useless at monitoring their use of magic; Harry, living at the Dursley's, would be given more attention, but it was stated Hermione has cast spells at home while underage without being reprimanded by the Ministry. So there are discrepencies in the books themselves. Also, in the books Tonks and Arthur Weasley both cast spells in Harry's home without the Ministry becoming involved. It is also theorized that the Ministry recognizes a discrepency between adult casting and underage casting; that said, considering Severus' history I don't doubt for a second he knows many ways to shield his presense from the notice of the Ministry even IF they were to be paying attention. And considering he's a man who flies under the law rather often, I imagine he's quite good at keeping off the radar.